diff --git a/onnxscript/function_libs/torch_aten/ops/core.py b/onnxscript/function_libs/torch_aten/ops/core.py
index 712791f934..91c834fee9 100644
--- a/onnxscript/function_libs/torch_aten/ops/core.py
+++ b/onnxscript/function_libs/torch_aten/ops/core.py
@@ -3257,10 +3257,58 @@ def aten_matrix_power(self: TensorType, n: int) -> TensorType:
     raise NotImplementedError()
 
 
-def aten_max(self: TensorType) -> TensorType:
+@torch_op("aten::max", trace_only=True)
+def aten_max(
+    self: TReal, dim_or_other: Union[TReal, INT64] = None, keepdim: BOOL = None
+) -> TReal:
     """max(Tensor self) -> Tensor"""
 
-    raise NotImplementedError()
+    self_rank = op.Size(op.Shape(self))
+    if self_rank == 0:
+        self = op.Reshape(self, op.Constant(value_int=[-1]))
+
+    output = 1
+
+    if op.OptionalHasElement(dim_or_other):
+        if isinstance(dim_or_other, int):
+            if not op.OptionalHasElement(keepdim):
+                keepdim = False
+            result, indices = _aten_max_with_dim(self, dim_or_other, keepdim)
+            output = 2
+        else:  # dim_or_other is tensor
+            result = _aten_max_with_other(self, dim_or_other)
+    else:
+        result = _aten_max_with_no_dim(self)
+
+    if self_rank == 0:
+        result = op.Squeeze(result)
+
+    if output == 2:
+        if self_rank == 0:
+            indices = op.Squeeze(indices)  # type: ignore[has-type]
+        return result, indices
+    return result
+
+
+@torch_op("aten::max", overload=True)
+def _aten_max_with_no_dim(self: TReal) -> TReal:
+    result = op.ReduceMax(self, keepdims=0)
+    return result
+
+
+@torch_op("aten::max", overload=True)
+def _aten_max_with_other(self: TReal, other: TReal) -> TReal:
+    result = op.Max(self, other)
+    return result
+
+
+@torch_op("aten::max", overload=True)
+# def _aten_max_with_dim(self: TReal, dim: int, keepdim: bool) -> tuple[TReal, TInt]:
+def _aten_max_with_dim(self: TReal, dim: int, keepdim: bool):
+    dims = op.Reshape(dim, op.Constant(value_int=[-1]))
+    result = op.ReduceMax(self, dims, keepdims=keepdim)
+    indices = op.ArgMax(self, axis=dim, keepdims=keepdim)
+    return result, indices
 
 
 def aten_max_pool1d(
diff --git a/onnxscript/tests/function_libs/torch_aten/ops_correctness_test.py b/onnxscript/tests/function_libs/torch_aten/ops_correctness_test.py
index aa26c20631..5df66b638f 100644
--- a/onnxscript/tests/function_libs/torch_aten/ops_correctness_test.py
+++ b/onnxscript/tests/function_libs/torch_aten/ops_correctness_test.py
@@ -398,6 +398,7 @@ def _where_input_wrangler(
     "convolution": core_ops.aten_convolution,
     "empty_like": core_ops.aten_empty_like,
     "index_select": core_ops.aten_index_select,
+    "max": core_ops.aten_max,
     "native_layer_norm": core_ops.aten_native_layer_norm,
     "new_empty": core_ops.aten_new_empty,
     "new_empty_strided": core_ops.aten_new_empty_strided,