diff --git a/docs/source/numpy.rst b/docs/source/numpy.rst
index 503c0ace4..5f5fc7699 100644
--- a/docs/source/numpy.rst
+++ b/docs/source/numpy.rst
@@ -136,8 +136,7 @@ See :any:`numpy indexing <numpy:arrays.indexing>` page.
 +====================================================================+====================================================================+
 | ``a[3, 2]``                                                        | ``a(3, 2)``                                                        |
 +--------------------------------------------------------------------+--------------------------------------------------------------------+
-| :any:`a.flat[4] <numpy.ndarray.flat>`                              || ``a[4]``                                                          |
-|                                                                    || ``a(4)``                                                          |
+| :any:`a.flat[4] <numpy.ndarray.flat>`                              | ``a.flat(4)``                                                      |
 +--------------------------------------------------------------------+--------------------------------------------------------------------+
 | ``a[3]``                                                           || ``xt::view(a, 3, xt::all())``                                     |
 |                                                                    || ``xt::row(a, 3)``                                                 |
diff --git a/include/xtensor/xaccessible.hpp b/include/xtensor/xaccessible.hpp
index 600ddd0b2..2f6af2c72 100644
--- a/include/xtensor/xaccessible.hpp
+++ b/include/xtensor/xaccessible.hpp
@@ -125,7 +125,7 @@ namespace xt
     /************************************
      * xconst_accessible implementation *
      ************************************/
-    
+
     /**
      * Returns the size of the expression.
      */
@@ -211,7 +211,7 @@ namespace xt
         normalize_periodic(derived_cast().shape(), args...);
         return derived_cast()(static_cast<size_type>(args)...);
     }
-    
+
     /**
      * Returns ``true`` only if the the specified position is a valid entry in the expression.
      * @param args a list of indices specifying the position in the expression.
@@ -246,7 +246,7 @@ namespace xt
     template <class D>
     template <class... Args>
     inline auto xaccessible<D>::at(Args... args) -> reference
-    {   
+    {
         check_access(derived_cast().shape(), static_cast<size_type>(args)...);
         return derived_cast().operator()(args...);
     }
@@ -293,7 +293,6 @@ namespace xt
         return derived_cast()(static_cast<size_type>(args)...);
     }
 
-
     template <class D>
     inline auto xaccessible<D>::derived_cast() noexcept -> derived_type&
     {
diff --git a/include/xtensor/xcontainer.hpp b/include/xtensor/xcontainer.hpp
index 7a116804c..df6ce6995 100644
--- a/include/xtensor/xcontainer.hpp
+++ b/include/xtensor/xcontainer.hpp
@@ -174,6 +174,9 @@ namespace xt
         reference data_element(size_type i);
         const_reference data_element(size_type i) const;
 
+        reference flat(size_type i);
+        const_reference flat(size_type i) const;
+
         template <class requested_type>
         using simd_return_type = xt_simd::simd_return_type<value_type, requested_type>;
 
@@ -643,6 +646,18 @@ namespace xt
         return storage()[i];
     }
 
+    template <class D>
+    inline auto xcontainer<D>::flat(size_type i) -> reference
+    {
+        return storage()[i];
+    }
+
+    template <class D>
+    inline auto xcontainer<D>::flat(size_type i) const -> const_reference
+    {
+        return storage()[i];
+    }
+
     /***************
      * stepper api *
      ***************/
diff --git a/include/xtensor/xdynamic_view.hpp b/include/xtensor/xdynamic_view.hpp
index 5c51d35b5..01a37a1d6 100644
--- a/include/xtensor/xdynamic_view.hpp
+++ b/include/xtensor/xdynamic_view.hpp
@@ -181,6 +181,9 @@ namespace xt
         template <class... Args>
         const_reference unchecked(Args... args) const;
 
+        reference flat(size_type index);
+        const_reference flat(size_type index) const;
+
         using base_type::operator[];
         using base_type::at;
         using base_type::periodic;
@@ -450,6 +453,18 @@ namespace xt
         return base_type::storage()[static_cast<size_type>(offset)];
     }
 
+    template <class CT, class S, layout_type L, class FST>
+    inline auto xdynamic_view<CT, S, L, FST>::flat(size_type i) -> reference
+    {
+        return base_type::storage()[data_offset() + i];
+    }
+
+    template <class CT, class S, layout_type L, class FST>
+    inline auto xdynamic_view<CT, S, L, FST>::flat(size_type i) const -> const_reference
+    {
+        return base_type::storage()[data_offset() + i];
+    }
+
     template <class CT, class S, layout_type L, class FST>
     template <class It>
     inline auto xdynamic_view<CT, S, L, FST>::element(It first, It last) -> reference
diff --git a/include/xtensor/xfunction.hpp b/include/xtensor/xfunction.hpp
index 5f1c4d7e0..49aa7a900 100644
--- a/include/xtensor/xfunction.hpp
+++ b/include/xtensor/xfunction.hpp
@@ -307,6 +307,8 @@ namespace xt
 
         const_reference data_element(size_type i) const;
 
+        const_reference flat(size_type i) const;
+
         template <class UT = self_type, class = typename std::enable_if<UT::only_scalar::value>::type>
         operator value_type() const;
 
@@ -583,6 +585,20 @@ namespace xt
         return access_impl(std::make_index_sequence<sizeof...(CT)>(), static_cast<size_type>(args)...);
     }
 
+    /**
+     * @name Data
+     */
+    /**
+     * Returns a constant reference to the element at the specified position of the underlying
+     * contiguous storage of the function.
+     * @param index index to underlying flat storage.
+     */
+    template <class F, class... CT>
+    inline auto xfunction<F, CT...>::flat(size_type index) const -> const_reference
+    {
+        return data_element_impl(std::make_index_sequence<sizeof...(CT)>(), index);
+    }
+
     /**
      * Returns a constant reference to the element at the specified position in the expression.
      * @param args a list of indices specifying the position in the expression. Indices
diff --git a/include/xtensor/xfunctor_view.hpp b/include/xtensor/xfunctor_view.hpp
index 9542c7065..b2b87921b 100644
--- a/include/xtensor/xfunctor_view.hpp
+++ b/include/xtensor/xfunctor_view.hpp
@@ -178,6 +178,7 @@ namespace xt
         using accessible_base::at;
         using accessible_base::operator[];
         using accessible_base::periodic;
+
         using accessible_base::in_bounds;
 
         xexpression_type& expression() noexcept;
@@ -203,6 +204,20 @@ namespace xt
             return m_functor(m_e.data_element(i));
         }
 
+        template <class FCT = functor_type>
+        auto flat(size_type i)
+            -> decltype(std::declval<FCT>()(std::declval<undecay_expression>().flat(i)))
+        {
+            return m_functor(m_e.flat(i));
+        }
+
+        template <class FCT = functor_type>
+        auto flat(size_type i) const
+            -> decltype(std::declval<FCT>()(std::declval<const undecay_expression>().flat(i)))
+        {
+            return m_functor(m_e.flat(i));
+        }
+
         // The following functions are defined inline because otherwise signatures
         // don't match on GCC.
         template <class align, class requested_type = typename xexpression_type::value_type,
@@ -732,7 +747,7 @@ namespace xt
      *
      * @warning This method is meant for performance, for expressions with a dynamic
      * number of dimensions (i.e. not known at compile time). Since it may have
-     * undefined behavior (see parameters), operator() should be prefered whenever
+     * undefined behavior (see parameters), operator() should be preferred whenever
      * it is possible.
      * @warning This method is NOT compatible with broadcasting, meaning the following
      * code has undefined behavior:
@@ -740,7 +755,7 @@ namespace xt
      * xt::xarray<double> a = {{0, 1}, {2, 3}};
      * xt::xarray<double> b = {0, 1};
      * auto fd = a + b;
-     * double res = fd.uncheked(0, 1);
+     * double res = fd.unchecked(0, 1);
      * \endcode
      */
     template <class D>
diff --git a/include/xtensor/xmasked_view.hpp b/include/xtensor/xmasked_view.hpp
index acd51ecd5..f0bebcc5b 100644
--- a/include/xtensor/xmasked_view.hpp
+++ b/include/xtensor/xmasked_view.hpp
@@ -37,7 +37,7 @@ namespace xt
 
     template <class CTD, class CTM>
     struct xcontainer_inner_types<xmasked_view<CTD, CTM>>
-    {   
+    {
         using data_type = std::decay_t<CTD>;
         using mask_type = std::decay_t<CTM>;
         using base_value_type = typename data_type::value_type;
diff --git a/include/xtensor/xoptional_assembly_base.hpp b/include/xtensor/xoptional_assembly_base.hpp
index 6e7c7ec10..67d34b612 100644
--- a/include/xtensor/xoptional_assembly_base.hpp
+++ b/include/xtensor/xoptional_assembly_base.hpp
@@ -177,6 +177,9 @@ namespace xt
         template <class... Args>
         const_reference periodic(Args... args) const;
 
+        reference flat(size_type args);
+        const_reference flat(size_type args) const;
+
         template <class It>
         reference element(It first, It last);
         template <class It>
@@ -659,6 +662,28 @@ namespace xt
         return const_reference(value().periodic(args...), has_value().periodic(args...));
     }
 
+    /**
+     * Returns a reference to the element at the specified position
+     * of the underlying storage in the optional assembly.
+     * @param index index to underlying flat storage.
+     */
+    template <class D>
+    inline auto xoptional_assembly_base<D>::flat(size_type i) -> reference
+    {
+        return reference(value().flat(i), has_value().flat(i));
+    }
+
+    /**
+     * Returns a constant reference to the element at the specified position
+     * of the underlying storage in the optional assembly.
+     * @param index index to underlying flat storage.
+     */
+    template <class D>
+    inline auto xoptional_assembly_base<D>::flat(size_type i) const -> const_reference
+    {
+        return const_reference(value().flat(i), has_value().flat(i));
+    }
+
     /**
      * Returns a reference to the element at the specified position in the optional assembly.
      * @param first iterator starting the sequence of indices
diff --git a/include/xtensor/xscalar.hpp b/include/xtensor/xscalar.hpp
index 83a1cb008..adb8591bf 100644
--- a/include/xtensor/xscalar.hpp
+++ b/include/xtensor/xscalar.hpp
@@ -281,6 +281,9 @@ namespace xt
         reference data_element(size_type i) noexcept;
         const_reference data_element(size_type i) const noexcept;
 
+        reference flat(size_type i) noexcept;
+        const_reference flat(size_type i) const noexcept;
+
         template <class align, class simd = simd_value_type>
         void store_simd(size_type i, const simd& e);
         template <class align, class requested_type = value_type,
@@ -932,6 +935,18 @@ namespace xt
         return m_value;
     }
 
+    template <class CT>
+    inline auto xscalar<CT>::flat(size_type) noexcept -> reference
+    {
+        return m_value;
+    }
+
+    template <class CT>
+    inline auto xscalar<CT>::flat(size_type) const noexcept -> const_reference
+    {
+        return m_value;
+    }
+
     template <class CT>
     template <class align, class simd>
     inline void xscalar<CT>::store_simd(size_type, const simd& e)
diff --git a/include/xtensor/xstrided_view.hpp b/include/xtensor/xstrided_view.hpp
index c6b05b6b9..7a6610595 100644
--- a/include/xtensor/xstrided_view.hpp
+++ b/include/xtensor/xstrided_view.hpp
@@ -266,6 +266,9 @@ namespace xt
         reference data_element(size_type i);
         const_reference data_element(size_type i) const;
 
+        reference flat(size_type i);
+        const_reference flat(size_type i) const;
+
         using container_iterator = std::conditional_t<is_const,
                                                       typename storage_type::const_iterator,
                                                       typename storage_type::iterator>;
@@ -457,6 +460,17 @@ namespace xt
         return storage()[i];
     }
 
+    template <class CT, class S, layout_type L, class FST>
+    inline auto xstrided_view<CT, S, L, FST>::flat(size_type i) -> reference
+    {
+        return storage()[i];
+    }
+
+    template <class CT, class S, layout_type L, class FST>
+    inline auto xstrided_view<CT, S, L, FST>::flat(size_type i) const -> const_reference
+    {
+        return storage()[i];
+    }
 
     template <class CT, class S, layout_type L, class FST>
     inline auto xstrided_view<CT, S, L, FST>::storage_begin() -> storage_iterator
diff --git a/include/xtensor/xview.hpp b/include/xtensor/xview.hpp
index 49e9c8ac3..eac650fc3 100644
--- a/include/xtensor/xview.hpp
+++ b/include/xtensor/xview.hpp
@@ -651,6 +651,12 @@ namespace xt
         template <class T = xexpression_type>
         enable_simd_interface<T, const_reference> data_element(size_type i) const;
 
+        template <class T = xexpression_type>
+        enable_simd_interface<T, reference> flat(size_type i);
+
+        template <class T = xexpression_type>
+        enable_simd_interface<T, const_reference> flat(size_type i) const;
+
     private:
 
         // VS 2015 workaround (yes, really)
@@ -1488,6 +1494,22 @@ namespace xt
         return m_e.data_element(data_offset() + i);
     }
 
+    template <class CT, class... S>
+    template <class T>
+    inline auto xview<CT, S...>::flat(size_type i) -> enable_simd_interface<T, reference>
+    {
+        XTENSOR_ASSERT(is_contiguous());
+        return m_e.flat(data_offset() + i);
+    }
+
+    template <class CT, class... S>
+    template <class T>
+    inline auto xview<CT, S...>::flat(size_type i) const -> enable_simd_interface<T, const_reference>
+    {
+        XTENSOR_ASSERT(is_contiguous());
+        return m_e.flat(data_offset() + i);
+    }
+
     template <class CT, class... S>
     template <class... Args>
     inline auto xview<CT, S...>::make_index_sequence(Args...) const noexcept
diff --git a/test/test_xarray.cpp b/test/test_xarray.cpp
index 2a23de052..d540069f2 100644
--- a/test/test_xarray.cpp
+++ b/test/test_xarray.cpp
@@ -324,6 +324,26 @@ namespace xt
         EXPECT_EQ(a, b);
     }
 
+    TEST(xarray, flat)
+    {
+        {
+            xt::xarray<size_t, xt::layout_type::row_major> a = {{0,1,2}, {3,4,5}};
+            xt::xarray<size_t, xt::layout_type::row_major> b = {{0,1,2}, {30,40,50}};
+            a.flat(3) = 30;
+            a.flat(4) = 40;
+            a.flat(5) = 50;
+            EXPECT_EQ(a, b);
+        }
+        {
+            xt::xarray<size_t, xt::layout_type::column_major> a = {{0,1,2}, {3,4,5}};
+            xt::xarray<size_t, xt::layout_type::column_major> b = {{0,1,2}, {30,40,50}};
+            a.flat(1) = 30;
+            a.flat(3) = 40;
+            a.flat(5) = 50;
+            EXPECT_EQ(a, b);
+        }
+    }
+
     TEST(xarray, in_bounds)
     {
         xt::xarray<size_t> a = {{0,1,2}, {3,4,5}};
diff --git a/test/test_xfunction.cpp b/test/test_xfunction.cpp
index ddd9ce824..4545f2d7b 100644
--- a/test/test_xfunction.cpp
+++ b/test/test_xfunction.cpp
@@ -271,6 +271,14 @@ namespace xt
         }
     }
 
+    TEST(xfunction, flat)
+    {
+        xfunction_features f;
+        int a = (f.m_a + f.m_a).flat(0);
+        int b = f.m_a.flat(0) + f.m_a.flat(0);
+        EXPECT_EQ(a, b);
+    }
+
     TEST(xfunction, in_bounds)
     {
         xfunction_features f;
diff --git a/test/test_xtensor.cpp b/test/test_xtensor.cpp
index 79e913374..1d8aedbdb 100644
--- a/test/test_xtensor.cpp
+++ b/test/test_xtensor.cpp
@@ -343,6 +343,26 @@ namespace xt
         EXPECT_EQ(a, b);
     }
 
+    TEST(xtensor, flat)
+    {
+        {
+            xt::xtensor<size_t, 2, xt::layout_type::row_major> a = {{0,1,2}, {3,4,5}};
+            xt::xtensor<size_t, 2, xt::layout_type::row_major> b = {{0,1,2}, {30,40,50}};
+            a.flat(3) = 30;
+            a.flat(4) = 40;
+            a.flat(5) = 50;
+            EXPECT_EQ(a, b);
+        }
+        {
+            xt::xtensor<size_t, 2, xt::layout_type::column_major> a = {{0,1,2}, {3,4,5}};
+            xt::xtensor<size_t, 2, xt::layout_type::column_major> b = {{0,1,2}, {30,40,50}};
+            a.flat(1) = 30;
+            a.flat(3) = 40;
+            a.flat(5) = 50;
+            EXPECT_EQ(a, b);
+        }
+    }
+
     TEST(xtensor, in_bounds)
     {
         xt::xtensor<size_t,2> a = {{0,1,2}, {3,4,5}};
diff --git a/test/test_xview.cpp b/test/test_xview.cpp
index fba27e703..2047c86eb 100644
--- a/test/test_xview.cpp
+++ b/test/test_xview.cpp
@@ -1464,6 +1464,17 @@ namespace xt
         EXPECT_EQ(a, b);
     }
 
+    TEST(xview, flat)
+    {
+        xt::xtensor<size_t, 2, xt::layout_type::row_major> a = {{0,1,2}, {3,4,5}};
+        xt::xtensor<size_t, 2, xt::layout_type::row_major> b = {{0,1,2}, {30,40,50}};
+        auto view = xt::view(a, 1, xt::all());
+        view.flat(0) = 30;
+        view.flat(1) = 40;
+        view.flat(2) = 50;
+        EXPECT_EQ(a, b);
+    }
+
     TEST(xview, in_bounds)
     {
         xt::xtensor<size_t,2> a = {{0,1,2}, {3,4,5}};