diff --git a/sdk/storage/azure-storage-blob/azure/storage/blob/_download.py b/sdk/storage/azure-storage-blob/azure/storage/blob/_download.py
index 58ac1c5b1b2b..a2f50ebc91ec 100644
--- a/sdk/storage/azure-storage-blob/azure/storage/blob/_download.py
+++ b/sdk/storage/azure-storage-blob/azure/storage/blob/_download.py
@@ -873,7 +873,7 @@ def content_as_bytes(self, max_concurrency=None):
 
         This method is deprecated, use func:`readall` instead.
 
-        :param int max_concurrency:
+        :param Optional[int] max_concurrency:
             The number of parallel connections with which to download.
         :return: The contents of the file as bytes.
         :rtype: bytes
@@ -896,7 +896,7 @@ def content_as_text(self, max_concurrency=None, encoding="UTF-8"):
 
         This method is deprecated, use func:`readall` instead.
 
-        :param int max_concurrency:
+        :param Optional[int] max_concurrency:
             The number of parallel connections with which to download.
         :param str encoding:
             Test encoding to decode the downloaded bytes. Default is UTF-8.
@@ -924,7 +924,7 @@ def download_to_stream(self, stream, max_concurrency=None):
             The stream to download to. This can be an open file-handle,
             or any writable stream. The stream must be seekable if the download
             uses more than one parallel connection.
-        :param int max_concurrency:
+        :param Optional[int] max_concurrency:
             The number of parallel connections with which to download.
         :return: The properties of the downloaded blob.
         :rtype: Any
diff --git a/sdk/storage/azure-storage-blob/azure/storage/blob/aio/_download_async.py b/sdk/storage/azure-storage-blob/azure/storage/blob/aio/_download_async.py
index 842b6dbc4320..30cbb0c68fbf 100644
--- a/sdk/storage/azure-storage-blob/azure/storage/blob/aio/_download_async.py
+++ b/sdk/storage/azure-storage-blob/azure/storage/blob/aio/_download_async.py
@@ -816,7 +816,7 @@ async def content_as_bytes(self, max_concurrency=None):
 
         This method is deprecated, use func:`readall` instead.
 
-        :param int max_concurrency:
+        :param Optional[int] max_concurrency:
             The number of parallel connections with which to download.
         :return: The contents of the file as bytes.
         :rtype: bytes
@@ -839,7 +839,7 @@ async def content_as_text(self, max_concurrency=None, encoding="UTF-8"):
 
         This method is deprecated, use func:`readall` instead.
 
-        :param int max_concurrency:
+        :param Optional[int] max_concurrency:
             The number of parallel connections with which to download.
         :param str encoding:
             Test encoding to decode the downloaded bytes. Default is UTF-8.
@@ -867,7 +867,7 @@ async def download_to_stream(self, stream, max_concurrency=None):
             The stream to download to. This can be an open file-handle,
             or any writable stream. The stream must be seekable if the download
             uses more than one parallel connection.
-        :param int max_concurrency:
+        :param Optional[int] max_concurrency:
             The number of parallel connections with which to download.
         :return: The properties of the downloaded blob.
         :rtype: Any