diff --git a/include/pybind11/numpy.h b/include/pybind11/numpy.h
index a26ac2b4cd..fd960f1dfa 100644
--- a/include/pybind11/numpy.h
+++ b/include/pybind11/numpy.h
@@ -1156,9 +1156,9 @@ class array : public buffer {
     }
 #endif
 
-    /// Dimension along a given axis
+    /// Dimension along a given axis. Throws if dim is negative or >= ndim() (no wrapping).
     ssize_t shape(ssize_t dim) const {
-        if (dim >= ndim()) {
+        if (dim < 0 || dim >= ndim()) {
             fail_dim_check(dim, "invalid axis");
         }
         return shape()[dim];
@@ -1174,9 +1174,9 @@ class array : public buffer {
     }
 #endif
 
-    /// Stride along a given axis
+    /// Stride along a given axis. Throws if dim is negative or >= ndim() (no wrapping).
     ssize_t strides(ssize_t dim) const {
-        if (dim >= ndim()) {
+        if (dim < 0 || dim >= ndim()) {
             fail_dim_check(dim, "invalid axis");
         }
         return strides()[dim];
@@ -1196,15 +1196,16 @@ class array : public buffer {
     }
 
     /// Pointer to the contained data. If index is not provided, points to the
-    /// beginning of the buffer. May throw if the index would lead to out of bounds access.
+    /// beginning of the buffer. Throws if an index is out of bounds; negative indices are not
+    /// wrapped.
     template <typename... Ix>
     const void *data(Ix... index) const {
         return static_cast<const void *>(detail::array_proxy(m_ptr)->data + offset_at(index...));
     }
 
     /// Mutable pointer to the contained data. If index is not provided, points to the
-    /// beginning of the buffer. May throw if the index would lead to out of bounds access.
-    /// May throw if the array is not writeable.
+    /// beginning of the buffer. Throws if an index is out of bounds; negative indices are not
+    /// wrapped. May throw if the array is not writeable.
     template <typename... Ix>
     void *mutable_data(Ix... index) {
         check_writeable();
@@ -1212,7 +1213,7 @@ class array : public buffer {
     }
 
     /// Byte offset from beginning of the array to a given index (full or partial).
-    /// May throw if the index would lead to out of bounds access.
+    /// Throws if an index is out of bounds; negative indices are not wrapped.
     template <typename... Ix>
     ssize_t offset_at(Ix... index) const {
         if ((ssize_t) sizeof...(index) > ndim()) {
@@ -1224,7 +1225,7 @@ class array : public buffer {
     ssize_t offset_at() const { return 0; }
 
     /// Item count from beginning of the array to a given index (full or partial).
-    /// May throw if the index would lead to out of bounds access.
+    /// Throws if an index is out of bounds; negative indices are not wrapped.
     template <typename... Ix>
     ssize_t index_at(Ix... index) const {
         return offset_at(index...) / itemsize();
@@ -1356,10 +1357,12 @@ class array : public buffer {
 
     template <typename... Ix>
     void check_dimensions_impl(ssize_t axis, const ssize_t *shape, ssize_t i, Ix... index) const {
-        if (i >= *shape) {
+        // Unsigned compare also rejects negative indices
+        if (static_cast<size_t>(i) >= static_cast<size_t>(*shape)) {
             throw index_error(std::string("index ") + std::to_string(i)
                               + " is out of bounds for axis " + std::to_string(axis)
-                              + " with size " + std::to_string(*shape));
+                              + " with size " + std::to_string(*shape)
+                              + (i < 0 ? " (negative indices are not supported)" : ""));
         }
         check_dimensions_impl(axis + 1, shape + 1, index...);
     }
@@ -1449,7 +1452,8 @@ class array_t : public array {
         return static_cast<T *>(array::mutable_data(index...));
     }
 
-    // Reference to element at a given index
+    // Reference to element at a given index. Throws if out of bounds; negative indices are not
+    // wrapped.
     template <typename... Ix>
     const T &at(Ix... index) const {
         if ((ssize_t) sizeof...(index) != ndim()) {
@@ -1459,7 +1463,8 @@ class array_t : public array {
                  + byte_offset(ssize_t(index)...) / itemsize());
     }
 
-    // Mutable reference to element at a given index
+    // Mutable reference to element at a given index. Throws if out of bounds; negative indices
+    // are not wrapped.
     template <typename... Ix>
     T &mutable_at(Ix... index) {
         if ((ssize_t) sizeof...(index) != ndim()) {
diff --git a/tests/test_numpy_array.py b/tests/test_numpy_array.py
index e3f29e92a6..2110c7c939 100644
--- a/tests/test_numpy_array.py
+++ b/tests/test_numpy_array.py
@@ -69,6 +69,12 @@ def test_array_attributes():
     with pytest.raises(IndexError) as excinfo:
         m.strides(a, 2)
     assert str(excinfo.value) == "invalid axis: 2 (ndim = 2)"
+    with pytest.raises(IndexError) as excinfo:
+        m.shape(a, -1)
+    assert str(excinfo.value) == "invalid axis: -1 (ndim = 2)"
+    with pytest.raises(IndexError) as excinfo:
+        m.strides(a, -1)
+    assert str(excinfo.value) == "invalid axis: -1 (ndim = 2)"
     assert not m.writeable(a)
     assert m.size(a) == 6
     assert m.itemsize(a) == 2
@@ -204,6 +210,8 @@ def test_bounds_check(arr):
     for func in (
         m.index_at,
         m.index_at_t,
+        m.offset_at,
+        m.offset_at_t,
         m.data,
         m.data_t,
         m.mutate_data,
@@ -217,6 +225,19 @@ def test_bounds_check(arr):
         with pytest.raises(IndexError) as excinfo:
             func(arr, 0, 4)
         assert str(excinfo.value) == "index 4 is out of bounds for axis 1 with size 3"
+        # Negative indices are not wrapped like in NumPy
+        with pytest.raises(IndexError) as excinfo:
+            func(arr, -1, 0)
+        assert (
+            str(excinfo.value)
+            == "index -1 is out of bounds for axis 0 with size 2 (negative indices are not supported)"
+        )
+        with pytest.raises(IndexError) as excinfo:
+            func(arr, 0, -1)
+        assert (
+            str(excinfo.value)
+            == "index -1 is out of bounds for axis 1 with size 3 (negative indices are not supported)"
+        )
 
 
 def test_make_c_f_array():