diff --git a/vllm/sequence.py b/vllm/sequence.py
index 13746cef..22cb26dc 100644
--- a/vllm/sequence.py
+++ b/vllm/sequence.py
@@ -39,24 +39,21 @@ PromptLogprobs = List[Optional[Dict[int, Logprob]]]
 SampleLogprobs = List[Dict[int, Logprob]]
 
 
-class SequenceStatus(enum.Enum):
+class SequenceStatus(enum.IntEnum):
     """Status of a sequence."""
-    WAITING = enum.auto()
-    RUNNING = enum.auto()
-    SWAPPED = enum.auto()
-    FINISHED_STOPPED = enum.auto()
-    FINISHED_LENGTH_CAPPED = enum.auto()
-    FINISHED_ABORTED = enum.auto()
-    FINISHED_IGNORED = enum.auto()
+    WAITING = 0
+    RUNNING = 1
+    SWAPPED = 2
+    # Note: anything after SWAPPED (2) will be considered
+    # as a finished status.
+    FINISHED_STOPPED = 3
+    FINISHED_LENGTH_CAPPED = 4
+    FINISHED_ABORTED = 5
+    FINISHED_IGNORED = 6
 
     @staticmethod
     def is_finished(status: "SequenceStatus") -> bool:
-        return status in [
-            SequenceStatus.FINISHED_STOPPED,
-            SequenceStatus.FINISHED_LENGTH_CAPPED,
-            SequenceStatus.FINISHED_ABORTED,
-            SequenceStatus.FINISHED_IGNORED,
-        ]
+        return status > SequenceStatus.SWAPPED
 
     @staticmethod
     def get_finished_reason(status: "SequenceStatus") -> Union[str, None]: