diff --git a/src/firebase_functions/private/path_pattern.py b/src/firebase_functions/private/path_pattern.py
index 78b61f0..bcf8bf6 100644
--- a/src/firebase_functions/private/path_pattern.py
+++ b/src/firebase_functions/private/path_pattern.py
@@ -129,9 +129,10 @@ class PathPattern:
     segments: list[PathSegment]
 
     def __init__(self, raw_path: str):
-        self.raw = raw_path
+        normalized_path = raw_path.strip("/")
+        self.raw = normalized_path
         self.segments = []
-        self.init_path_segments(raw_path)
+        self.init_path_segments(normalized_path)
 
     def init_path_segments(self, raw: str):
         parts = raw.split("/")
diff --git a/tests/test_path_pattern.py b/tests/test_path_pattern.py
index 5248b02..3513e34 100644
--- a/tests/test_path_pattern.py
+++ b/tests/test_path_pattern.py
@@ -41,6 +41,28 @@ def test_trim_param(self):
         self.assertEqual(trim_param("{something=*}"), "something")
 
     def test_extract_matches(self):
+        # parse single-capture segments with leading slash
+        pp = PathPattern("/messages/{a}/{b}/{c}")
+        self.assertEqual(
+            pp.extract_matches("messages/match_a/match_b/match_c"),
+            {
+                "a": "match_a",
+                "b": "match_b",
+                "c": "match_c",
+            },
+        )
+
+        # parse single-capture segments without leading slash
+        pp = PathPattern("messages/{a}/{b}/{c}")
+        self.assertEqual(
+            pp.extract_matches("messages/match_a/match_b/match_c"),
+            {
+                "a": "match_a",
+                "b": "match_b",
+                "c": "match_c",
+            },
+        )
+
         # parse without multi-capture segments
         pp = PathPattern("{a}/something/else/{b}/end/{c}")
         self.assertEqual(