diff --git a/replicate/client.py b/replicate/client.py
index 6a79813..a89fc30 100644
--- a/replicate/client.py
+++ b/replicate/client.py
@@ -2,7 +2,8 @@
 import os
 import random
 import time
-from datetime import datetime
+from datetime import datetime, timezone
+from email.utils import parsedate_to_datetime
 from typing import (
     TYPE_CHECKING,
     Any,
@@ -277,11 +278,18 @@ def _calculate_sleep(
                 return float(retry_after_header)
 
             try:
-                parsed_date = datetime.fromisoformat(retry_after_header).astimezone()
+                try:
+                    parsed_date = datetime.fromisoformat(
+                        retry_after_header
+                    ).astimezone()
+                except ValueError:
+                    parsed_date = parsedate_to_datetime(retry_after_header)
+                    if parsed_date.tzinfo is None:
+                        parsed_date = parsed_date.replace(tzinfo=timezone.utc)
                 diff = (parsed_date - datetime.now().astimezone()).total_seconds()
                 if diff > 0:
                     return min(diff, self.max_backoff_wait)
-            except ValueError:
+            except (TypeError, ValueError, OverflowError):
                 pass
 
         backoff = self.backoff_factor * (2 ** (attempts_made - 1))
diff --git a/tests/test_retry_after.py b/tests/test_retry_after.py
new file mode 100644
index 0000000..b07cfa5
--- /dev/null
+++ b/tests/test_retry_after.py
@@ -0,0 +1,90 @@
+from datetime import datetime, timezone
+
+import httpx
+import pytest
+
+from replicate import client as client_module
+from replicate.client import RetryTransport
+
+
+class FixedDateTime(datetime):
+    @classmethod
+    def now(cls, tz=None) -> datetime:
+        return datetime(2026, 10, 18, 12, 0, 0, tzinfo=timezone.utc).astimezone(tz)
+
+
+CASES = [
+    ("Sun, 18 Oct 2026 12:00:30 GMT", 30),
+    ("Sunday, 18-Oct-26 12:00:30 GMT", 30),
+    ("Sun Oct 18 12:00:30 2026", 30),
+    ("Sun, 18 Oct 2026 12:01:30 GMT", 60),
+    ("2026-10-18T12:00:30+00:00", 30),
+    ("Sun, 18 Oct 2026 11:59:30 GMT", 0.1),
+    ("invalid", 0.1),
+    ("", 0.1),
+    ("0", 0),
+    ("3", 3),
+    ("120", 120),
+]
+
+
+@pytest.mark.parametrize("header,expected", CASES)
+@pytest.mark.parametrize("status", [429, 503])
+def test_retry_after_sync(monkeypatch, header, expected, status):
+    monkeypatch.setattr(client_module, "datetime", FixedDateTime)
+    sleeps = []
+    monkeypatch.setattr(client_module.time, "sleep", sleeps.append)
+    responses = [
+        httpx.Response(status, headers={"Retry-After": header}),
+        httpx.Response(200, json={"ok": True}),
+    ]
+    attempts = []
+
+    def respond(request):
+        attempts.append(request)
+        return responses[len(attempts) - 1]
+
+    with httpx.Client(
+        transport=RetryTransport(
+            httpx.MockTransport(respond), max_attempts=2, jitter_ratio=0
+        )
+    ) as client:
+        response = client.get("https://example.test/predictions")
+
+    assert response.json() == {"ok": True}
+    assert sleeps == [expected]
+    assert len(attempts) == 2
+    assert responses[0].is_closed
+
+
+@pytest.mark.parametrize("header,expected", CASES)
+@pytest.mark.parametrize("status", [429, 503])
+async def test_retry_after_async(monkeypatch, header, expected, status):
+    monkeypatch.setattr(client_module, "datetime", FixedDateTime)
+    sleeps = []
+
+    async def sleep(delay):
+        sleeps.append(delay)
+
+    monkeypatch.setattr(client_module.asyncio, "sleep", sleep)
+    responses = [
+        httpx.Response(status, headers={"Retry-After": header}),
+        httpx.Response(200, json={"ok": True}),
+    ]
+    attempts = []
+
+    def respond(request):
+        attempts.append(request)
+        return responses[len(attempts) - 1]
+
+    async with httpx.AsyncClient(
+        transport=RetryTransport(
+            httpx.MockTransport(respond), max_attempts=2, jitter_ratio=0
+        )
+    ) as client:
+        response = await client.get("https://example.test/predictions")
+
+    assert response.json() == {"ok": True}
+    assert sleeps == [expected]
+    assert len(attempts) == 2
+    assert responses[0].is_closed