diff --git a/Lib/logging/handlers.py b/Lib/logging/handlers.py
index 472eee5f6cc..f8c7164bc18 100644
--- a/Lib/logging/handlers.py
+++ b/Lib/logging/handlers.py
@@ -125,6 +125,7 @@ class RotatingFileHandler(BaseRotatingHandler):
         """
         if self.stream:
             self.stream.close()
+            self.stream = None
         if self.backupCount > 0:
             for i in range(self.backupCount - 1, 0, -1):
                 sfn = "%s.%d" % (self.baseFilename, i)
@@ -324,6 +325,7 @@ class TimedRotatingFileHandler(BaseRotatingHandler):
         """
         if self.stream:
             self.stream.close()
+            self.stream = None
         # get the time that this sequence started at and make it a TimeTuple
         t = self.rolloverAt - self.interval
         if self.utc:
diff --git a/Misc/NEWS b/Misc/NEWS
index b9205de1f99..f77b60354e1 100644
--- a/Misc/NEWS
+++ b/Misc/NEWS
@@ -35,6 +35,8 @@ Core and Builtins
 Library
 -------
 
+- Issue #10949: Improved robustness of rotating file handlers.
+
 - Issue #10955: Fix a potential crash when trying to mmap() a file past its
   length.  Initial patch by Ross Lagerwall.