diff --git a/pyproject.toml b/pyproject.toml
index 27a745615..4a9557789 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -59,7 +59,7 @@ nvcc = [
 
 [build-system]
 requires = [
-    "cython>=3.0.0",
+    "cython>=3.1.0",
     "scikit-build-core",
     "z3-solver>=4.13.0",
     # Not for auditwheel, explicitly add patchelf for repairing libz3.so.
diff --git a/tilelang/_typing.py b/tilelang/_typing.py
index c2c3fce1d..e834d7916 100644
--- a/tilelang/_typing.py
+++ b/tilelang/_typing.py
@@ -11,6 +11,8 @@
 except ImportError:  # Python < 3.10
     from typing_extensions import TypeAlias
 
+from typing import Union
+
 from tvm import ir
 from tvm import tir
 
@@ -18,10 +20,10 @@
 from tilelang.dtypes import dtype
 
 # Barrier can only be a Buffer, a BufferLoad
-BarrierType: TypeAlias = tir.Buffer | BufferLoad
+BarrierType: TypeAlias = Union[tir.Buffer, BufferLoad]
 
 # BufferLikeType can be a Buffer, a BufferLoad, a BufferRegion
-BufferLikeType: TypeAlias = tir.Buffer | BufferLoad | BufferRegion
+BufferLikeType: TypeAlias = Union[tir.Buffer, BufferLoad, BufferRegion]
 
 # This is for Python 3.9 compatibility.
 # In Python 3.9, we can only use isinstance(a, (TypeA, TypeB, ...)) instead of isinstance(a, TypeA | TypeB | ...))
@@ -31,5 +33,5 @@
 # - AnyDType is a union of all possible types that can represent a data type, including torch.dtype
 # - DType is a more specific type alias that represents a data type in the context of TileLang, and must be
 #   adapted to string.
-DType: TypeAlias = dtype | ir.Type | str | type
-ShapeType: TypeAlias = list[tir.PrimExpr | int] | tuple[tir.PrimExpr | int, ...]
+DType: TypeAlias = Union[dtype, ir.Type, str, type]
+ShapeType: TypeAlias = Union[list[Union[tir.PrimExpr, int]], tuple[Union[tir.PrimExpr, int], ...]]