diff --git a/python/test/unit/language/test_block_pointer.py b/python/test/unit/language/test_block_pointer.py
index 8e84a9f82a08..aff7a29d8781 100644
--- a/python/test/unit/language/test_block_pointer.py
+++ b/python/test/unit/language/test_block_pointer.py
@@ -7,29 +7,36 @@
 
 
 @triton.jit
-def block_copy_kernel(a_ptr, b_ptr, N, BLOCK_SIZE: tl.constexpr, padding_option: tl.constexpr):
+def block_copy_kernel(a_ptr, b_ptr, N, BLOCK_SIZE: tl.constexpr, PADDING_OPTION: tl.constexpr,
+                      TEST_LOWER_BOUND: tl.constexpr, TEST_UPPER_BOUND: tl.constexpr):
     pid = tl.program_id(0)
+    offset = pid * BLOCK_SIZE
+    if TEST_LOWER_BOUND:
+        offset = -N
+    elif TEST_UPPER_BOUND:
+        offset = N
     # We only copy half of the data to see if the padding works
-    a_block_ptr = tl.make_block_ptr(base=a_ptr, shape=(N // 2, ), strides=(1, ), offsets=(pid * BLOCK_SIZE, ),
+    a_block_ptr = tl.make_block_ptr(base=a_ptr, shape=(N // 2, ), strides=(1, ), offsets=(offset, ),
                                     block_shape=(BLOCK_SIZE, ), order=(0, ))
-    b_block_ptr = tl.make_block_ptr(base=b_ptr, shape=(N, ), strides=(1, ), offsets=(pid * BLOCK_SIZE, ),
+    b_block_ptr = tl.make_block_ptr(base=b_ptr, shape=(N, ), strides=(1, ), offsets=(offset, ),
                                     block_shape=(BLOCK_SIZE, ), order=(0, ))
-    if padding_option is None:
+    if PADDING_OPTION is None:
         a = tl.load(a_block_ptr, boundary_check=(0, ))
     else:
-        a = tl.load(a_block_ptr, boundary_check=(0, ), padding_option=padding_option)
+        a = tl.load(a_block_ptr, boundary_check=(0, ), padding_option=PADDING_OPTION)
     tl.store(b_block_ptr, a, boundary_check=(0, ))
 
 
 @pytest.mark.interpreter
-@pytest.mark.parametrize("dtypes_str, n, padding_option", [  #
-    (dtypes_str, n, padding)
+@pytest.mark.parametrize("dtypes_str, n, padding_option, boundary_check", [  #
+    (dtypes_str, n, padding, boundary_check)  #
     for dtypes_str in (("bool", "bool"), ("int16", "int16"), ("int32", "int32"), ("float16", "float16"),
                        ("float32", "float32"), ("bfloat16", "bfloat16"))
     for n in (64, 128, 256, 512, 1024)
     for padding in (None, "zero", "nan")  #
+    for boundary_check in (None, "lower", "upper")
 ])
-def test_block_copy(dtypes_str, n, padding_option, device):
+def test_block_copy(dtypes_str, n, padding_option, boundary_check, device):
     src_dtype_str = dtypes_str[0]
     dst_dtype_str = dtypes_str[1]
     src_dtype = getattr(torch, src_dtype_str)
@@ -45,13 +52,17 @@ def test_block_copy(dtypes_str, n, padding_option, device):
     b = torch.zeros((n, ), device=device, dtype=dst_dtype)
 
     grid = lambda meta: (triton.cdiv(n, meta["BLOCK_SIZE"]), )
-    block_copy_kernel[grid](a_ptr=a, b_ptr=b, N=n, BLOCK_SIZE=64, padding_option=padding_option)
+    block_copy_kernel[grid](a_ptr=a, b_ptr=b, N=n, BLOCK_SIZE=64, PADDING_OPTION=padding_option,
+                            TEST_LOWER_BOUND=boundary_check == "lower", TEST_UPPER_BOUND=boundary_check == "upper")
     a.to(dst_dtype)
-    assert torch.all(a[0:n // 2] == b[0:n // 2])
-    if padding_option == "zero":
-        assert torch.all(b[n // 2:n] == 0)
-    elif padding_option == "nan":
-        assert torch.all(torch.isnan(b[n // 2:n]))
+    if (boundary_check == "lower") or (boundary_check == "upper"):
+        assert torch.all(b == 0)
+    else:
+        assert torch.all(a[0:n // 2] == b[0:n // 2])
+        if padding_option == "zero":
+            assert torch.all(b[n // 2:n] == 0)
+        elif padding_option == "nan":
+            assert torch.all(torch.isnan(b[n // 2:n]))
 
 
 @triton.jit
diff --git a/python/triton/runtime/interpreter.py b/python/triton/runtime/interpreter.py
index b85cc2e9aec7..3b94f55ea3c0 100644
--- a/python/triton/runtime/interpreter.py
+++ b/python/triton/runtime/interpreter.py
@@ -65,7 +65,7 @@ def materialize_pointers(self, boundary_check):
             off = (self.offsets[dim].data + np.arange(self.block_shape[dim])).reshape(bcast_dims)
             ptrs = ptrs + (n_bytes * off * self.strides[dim].data).astype(np.uint64)
             if dim in boundary_check:
-                masks = np.logical_and(masks, off < self.shape[dim].data)
+                masks = masks & (off < self.shape[dim].data) & (off >= 0)
         ptrs = TensorHandle(ptrs, self.base.dtype.scalar)
         return ptrs, masks