diff --git a/tenacity/retry.py b/tenacity/retry.py
index df0cc4d6..e4b5a274 100644
--- a/tenacity/retry.py
+++ b/tenacity/retry.py
@@ -241,7 +241,12 @@ def _check(self, exception: BaseException) -> bool:
         if self.message:
             return self.message == str(exception)
         assert self.match is not None
-        return bool(self.match.match(str(exception)))
+        # Use re.search (not re.match) so the pattern is found anywhere in
+        # the exception message. re.match only matches at the start, so a
+        # user-supplied pattern like r"rate limit" would never match
+        # "HTTP 429: rate limit hit". The parameter is named ``match``,
+        # meaning "find a match in the message", not "match from offset 0".
+        return bool(self.match.search(str(exception)))
 
 
 class retry_if_not_exception_message(retry_if_exception_message):
diff --git a/tests/test_tenacity.py b/tests/test_tenacity.py
index 9ecdea56..82540717 100644
--- a/tests/test_tenacity.py
+++ b/tests/test_tenacity.py
@@ -1173,10 +1173,10 @@ def _retryable_test_with_unless_exception_type_no_input(
 
 
 @retry(
-    stop=tenacity.stop_after_attempt(5),
     retry=tenacity.retry_if_exception_message(
         message=NoCustomErrorAfterCount.derived_message
     ),
+    stop=tenacity.stop_after_attempt(5),
 )
 def _retryable_test_if_exception_message_message(thing: typing.Any) -> typing.Any:
     return thing.go()
@@ -1209,6 +1209,14 @@ def _retryable_test_if_not_exception_message_match(thing: typing.Any) -> typing.
     return thing.go()
 
 
+@retry(
+    retry=tenacity.retry_if_exception_message(match="limit exceeded"),
+    stop=tenacity.stop_after_attempt(5),
+)
+def _retryable_test_if_exception_message_match_search(thing: typing.Any) -> typing.Any:
+    return thing.go()
+
+
 @retry(
     retry=tenacity.retry_if_not_exception_message(
         message=NameErrorUntilCount.derived_message
@@ -1378,6 +1386,36 @@ def test_retry_if_exception_message_match(self) -> None:
         except CustomError:
             self.fail("CustomError should've been retried from errormessage")
 
+    def test_retry_if_exception_message_match_finds_pattern_anywhere(self) -> None:
+        # Regression: the `match` kwarg used to call re.Pattern.match(), which
+        # only matches at the start of the message. A user who wrote
+        # `match="limit exceeded"` to catch `"HTTP 429: rate limit exceeded"`
+        # got zero retries because the pattern was not anchored at index 0.
+        # The fix uses re.Pattern.search() so the pattern is found anywhere
+        # in the message, which is what the parameter name implies.
+        class MessageCount:
+            derived_message = "HTTP 429: rate limit exceeded"
+
+            def __init__(self, count: int) -> None:
+                self.counter = 0
+                self.count = count
+
+            def go(self) -> bool:
+                if self.counter < self.count:
+                    self.counter += 1
+                    raise CustomError(self.derived_message)
+                return True
+
+        try:
+            self.assertTrue(
+                _retryable_test_if_exception_message_match_search(MessageCount(3))
+            )
+        except CustomError:
+            self.fail(
+                "CustomError should've been retried: the 'limit exceeded' pattern "
+                "appears in the message and should trigger a retry"
+            )
+
     def test_retry_if_not_exception_message_match(self) -> None:
         try:
             self.assertTrue(