diff --git a/pandas/core/arrays/_mixins.py b/pandas/core/arrays/_mixins.py
index 57df9ed9ed2d7..ad0bf76b0556b 100644
--- a/pandas/core/arrays/_mixins.py
+++ b/pandas/core/arrays/_mixins.py
@@ -369,8 +369,16 @@ def where(
         res_values = np.where(mask, self._ndarray, value)
         return self._from_backing_data(res_values)
 
-    def delete(self: NDArrayBackedExtensionArrayT, loc) -> NDArrayBackedExtensionArrayT:
-        res_values = np.delete(self._ndarray, loc)
+    def delete(
+        self: NDArrayBackedExtensionArrayT, loc, axis: int = 0
+    ) -> NDArrayBackedExtensionArrayT:
+        res_values = np.delete(self._ndarray, loc, axis=axis)
+        return self._from_backing_data(res_values)
+
+    def swapaxes(
+        self: NDArrayBackedExtensionArrayT, axis1, axis2
+    ) -> NDArrayBackedExtensionArrayT:
+        res_values = self._ndarray.swapaxes(axis1, axis2)
         return self._from_backing_data(res_values)
 
     # ------------------------------------------------------------------------
diff --git a/pandas/tests/extension/base/dim2.py b/pandas/tests/extension/base/dim2.py
index c6455ce15533a..fbe2537e8a7bf 100644
--- a/pandas/tests/extension/base/dim2.py
+++ b/pandas/tests/extension/base/dim2.py
@@ -25,6 +25,26 @@ def maybe_xfail_masked_reductions(arr, request):
 
 
 class Dim2CompatTests(BaseExtensionTests):
+    def test_swapaxes(self, data):
+        arr2d = data.repeat(2).reshape(-1, 2)
+
+        result = arr2d.swapaxes(0, 1)
+        expected = arr2d.T
+        self.assert_extension_array_equal(result, expected)
+
+    def test_delete_2d(self, data):
+        arr2d = data.repeat(3).reshape(-1, 3)
+
+        # axis = 0
+        result = arr2d.delete(1, axis=0)
+        expected = data.delete(1).repeat(3).reshape(-1, 3)
+        self.assert_extension_array_equal(result, expected)
+
+        # axis = 1
+        result = arr2d.delete(1, axis=1)
+        expected = data.repeat(2).reshape(-1, 2)
+        self.assert_extension_array_equal(result, expected)
+
     def test_take_2d(self, data):
         arr2d = data.reshape(-1, 1)