diff --git a/test/onnx/test_pytorch_onnx_onnxruntime.py b/test/onnx/test_pytorch_onnx_onnxruntime.py
index 3c741fb8845..4e39baf3227 100644
--- a/test/onnx/test_pytorch_onnx_onnxruntime.py
+++ b/test/onnx/test_pytorch_onnx_onnxruntime.py
@@ -175,6 +175,16 @@ class TestONNXRuntime(unittest.TestCase):
         x = {"test_key_in": torch.randn(1, 2, 3)}
         self.run_test(MyModel(), (x,))
 
+    @skipIfUnsupportedMinOpsetVersion(9)
+    def test_cste_script(self):
+        class MyModel(torch.jit.ScriptModule):
+            @torch.jit.script_method
+            def forward(self, x):
+                return torch.zeros(x.size(0)), torch.ones((x.size(1), x.size(0)), dtype=torch.int64)
+
+        x = torch.randn(3, 4)
+        self.run_test(MyModel(), x)
+
     def test_clamp(self):
         class ClampModel(torch.nn.Module):
             def forward(self, x):
diff --git a/torch/onnx/symbolic_helper.py b/torch/onnx/symbolic_helper.py
index 048e69c36c1..762e0a393ac 100644
--- a/torch/onnx/symbolic_helper.py
+++ b/torch/onnx/symbolic_helper.py
@@ -54,6 +54,8 @@ def _parse_arg(value, desc):
         return value
     if desc == 'v' or not _is_value(value):
         return value
+    if value.node().mustBeNone():
+        return None
     if value.node().kind() == 'onnx::Constant':
         tval = value.node()['value']
         if desc == 'i':
diff --git a/torch/onnx/symbolic_opset8.py b/torch/onnx/symbolic_opset8.py
index 52a48d2fa58..4da2bc1ead5 100644
--- a/torch/onnx/symbolic_opset8.py
+++ b/torch/onnx/symbolic_opset8.py
@@ -205,6 +205,8 @@ def flatten(g, input, start_dim, end_dim):
 
 
 def _constant_fill(g, sizes, dtype, const_value):
+    if dtype is None:
+        dtype = 6  # float
     if not sym_help.scalar_type_to_pytorch_type[dtype].is_floating_point:
         result = g.op(
             "ConstantFill", sizes, dtype_i=sym_help.cast_pytorch_to_onnx["Float"], input_as_shape_i=1, value_f=const_value)
diff --git a/torch/onnx/symbolic_opset9.py b/torch/onnx/symbolic_opset9.py
index 19dd546ecc8..2ceee200806 100644
--- a/torch/onnx/symbolic_opset9.py
+++ b/torch/onnx/symbolic_opset9.py
@@ -1215,6 +1215,8 @@ def empty_like(g, input, dtype, layout, device, pin_memory=False, memory_format=
 @parse_args('v', 'i', 'v', 'v', 'v')
 def zeros(g, sizes, dtype, layout, device, pin_memory=False):
     # NOTE: no way to set device, layout and pin_memory in ONNX, so we ignore it
+    if dtype is None:
+        dtype = 6  # float
     return g.op("ConstantOfShape", sizes,
                 value_t=torch.tensor([0], dtype=sym_help.scalar_type_to_pytorch_type[dtype]))
 
@@ -1222,12 +1224,16 @@ def zeros(g, sizes, dtype, layout, device, pin_memory=False):
 @parse_args('v', 'i', 'v', 'v', 'v')
 def zeros_like(g, input, dtype, layout, device, pin_memory=False):
     shape = g.op("Shape", input)
+    if dtype is None:
+        dtype = 6  # float
     return g.op("ConstantOfShape", shape,
                 value_t=torch.tensor([0], dtype=sym_help.scalar_type_to_pytorch_type[dtype]))
 
 
 @parse_args('v', 'i', 'v', 'v', 'v')
 def ones(g, sizes, dtype, layout, device, pin_memory=False):
+    if dtype is None:
+        dtype = 6  # float
     return g.op("ConstantOfShape", sizes,
                 value_t=torch.tensor([1], dtype=sym_help.scalar_type_to_pytorch_type[dtype]))
 
@@ -1235,11 +1241,15 @@ def ones(g, sizes, dtype, layout, device, pin_memory=False):
 @parse_args('v', 'i', 'v', 'v', 'v')
 def ones_like(g, input, dtype, layout, device, pin_memory=False):
     shape = g.op("Shape", input)
+    if dtype is None:
+        dtype = 6  # float
     return g.op("ConstantOfShape", shape,
                 value_t=torch.tensor([1], dtype=sym_help.scalar_type_to_pytorch_type[dtype]))
 
 
 def full(g, sizes, value, dtype, layout, device, pin_memory=False):
+    if dtype is None:
+        dtype = 6  # float
     const_value = sym_help._maybe_get_const(value, 't')
     if sym_help._is_value(const_value):
         tmp = zeros(g, sizes, dtype, layout, device)
@@ -1253,6 +1263,8 @@ def full(g, sizes, value, dtype, layout, device, pin_memory=False):
 @parse_args('v', 'f', 'i', 'v', 'v', 'v')
 def full_like(g, input, fill_value, dtype, layout, device, pin_memory=False):
     shape = g.op("Shape", input)
+    if dtype is None:
+        dtype = 6  # float
     return g.op("ConstantOfShape", shape,
                 value_t=torch.tensor([fill_value], dtype=sym_help.scalar_type_to_pytorch_type[dtype]))