diff --git a/Lib/test/test_gdb.py b/Lib/test/test_gdb.py
index 1a9975fb84d1e9..0131e4d0b0f72d 100644
--- a/Lib/test/test_gdb.py
+++ b/Lib/test/test_gdb.py
@@ -227,6 +227,15 @@ def get_stack_trace(self, source=None, script=None,
                                     " because the Program Counter is"
                                     " not present")
 
+        # bpo-40019: Skip the test if gdb failed to read debug information
+        # because the Python binary is optimized.
+        for pattern in (
+            '(frame information optimized out)',
+            'Unable to read information on python frame',
+        ):
+            if pattern in out:
+                raise unittest.SkipTest(f"{pattern!r} found in gdb output")
+
         return out
 
     def get_gdb_repr(self, source,
diff --git a/Misc/NEWS.d/next/Tests/2020-03-20-00-30-36.bpo-40019.zOqHpQ.rst b/Misc/NEWS.d/next/Tests/2020-03-20-00-30-36.bpo-40019.zOqHpQ.rst
new file mode 100644
index 00000000000000..a9d0b3970ae537
--- /dev/null
+++ b/Misc/NEWS.d/next/Tests/2020-03-20-00-30-36.bpo-40019.zOqHpQ.rst
@@ -0,0 +1,2 @@
+test_gdb now skips tests if it detects that gdb failed to read debug
+information because the Python binary is optimized.
diff --git a/Tools/gdb/libpython.py b/Tools/gdb/libpython.py
index feec789e6ade93..86ace3796218f8 100755
--- a/Tools/gdb/libpython.py
+++ b/Tools/gdb/libpython.py
@@ -99,6 +99,8 @@ def _sizeof_void_p():
 
 ENCODING = locale.getpreferredencoding()
 
+FRAME_INFO_OPTIMIZED_OUT = '(frame information optimized out)'
+UNABLE_READ_INFO_PYTHON_FRAME = 'Unable to read information on python frame'
 EVALFRAME = '_PyEval_EvalFrameDefault'
 
 class NullPyObjectPtr(RuntimeError):
@@ -918,7 +920,7 @@ def get_var_by_name(self, name):
     def filename(self):
         '''Get the path of the current Python source file, as a string'''
         if self.is_optimized_out():
-            return '(frame information optimized out)'
+            return FRAME_INFO_OPTIMIZED_OUT
         return self.co_filename.proxyval(set())
 
     def current_line_num(self):
@@ -949,7 +951,7 @@ def current_line(self):
         '''Get the text of the current source line as a string, with a trailing
         newline character'''
         if self.is_optimized_out():
-            return '(frame information optimized out)'
+            return FRAME_INFO_OPTIMIZED_OUT
 
         lineno = self.current_line_num()
         if lineno is None:
@@ -970,7 +972,7 @@ def current_line(self):
 
     def write_repr(self, out, visited):
         if self.is_optimized_out():
-            out.write('(frame information optimized out)')
+            out.write(FRAME_INFO_OPTIMIZED_OUT)
             return
         lineno = self.current_line_num()
         lineno = str(lineno) if lineno is not None else "?"
@@ -993,7 +995,7 @@ def write_repr(self, out, visited):
 
     def print_traceback(self):
         if self.is_optimized_out():
-            sys.stdout.write('  (frame information optimized out)\n')
+            sys.stdout.write('  %s\n' % FRAME_INFO_OPTIMIZED_OUT)
             return
         visited = set()
         lineno = self.current_line_num()
@@ -1744,7 +1746,7 @@ def invoke(self, args, from_tty):
 
         pyop = frame.get_pyop()
         if not pyop or pyop.is_optimized_out():
-            print('Unable to read information on python frame')
+            print(UNABLE_READ_INFO_PYTHON_FRAME)
             return
 
         filename = pyop.filename()
@@ -1904,7 +1906,7 @@ def invoke(self, args, from_tty):
 
         pyop_frame = frame.get_pyop()
         if not pyop_frame:
-            print('Unable to read information on python frame')
+            print(UNABLE_READ_INFO_PYTHON_FRAME)
             return
 
         pyop_var, scope = pyop_frame.get_var_by_name(name)
@@ -1938,7 +1940,7 @@ def invoke(self, args, from_tty):
 
         pyop_frame = frame.get_pyop()
         if not pyop_frame:
-            print('Unable to read information on python frame')
+            print(UNABLE_READ_INFO_PYTHON_FRAME)
             return
 
         for pyop_name, pyop_value in pyop_frame.iter_locals():