diff --git a/packaging/markers.py b/packaging/markers.py
index 399051489..1d61adaff 100644
--- a/packaging/markers.py
+++ b/packaging/markers.py
@@ -5,6 +5,7 @@
 import operator
 import os
 import platform
+import re
 import sys
 from typing import Any, Callable, Dict, List, Optional, Tuple, Union
 
@@ -219,6 +220,16 @@ def _get_env(environment: Dict[str, str], name: str) -> str:
     return value
 
 
+def _normalize(*values: str, key: str) -> Tuple[str, ...]:
+    # PEP 685 – Comparison of extra names for optional distribution dependencies
+    # https://peps.python.org/pep-0685/
+    if key == "extra":
+        return tuple(re.sub(r"[-_.]+", "-", v).lower() for v in values)
+
+    # other environment markes don't have such standards
+    return values
+
+
 def _evaluate_markers(markers: List[Any], environment: Dict[str, str]) -> bool:
     groups: List[List[bool]] = [[]]
 
@@ -231,12 +242,15 @@ def _evaluate_markers(markers: List[Any], environment: Dict[str, str]) -> bool:
             lhs, op, rhs = marker
 
             if isinstance(lhs, Variable):
-                lhs_value = _get_env(environment, lhs.value)
+                environment_key = lhs.value
+                lhs_value = _get_env(environment, environment_key)
                 rhs_value = rhs.value
             else:
                 lhs_value = lhs.value
-                rhs_value = _get_env(environment, rhs.value)
+                environment_key = rhs.value
+                rhs_value = _get_env(environment, environment_key)
 
+            lhs_value, rhs_value = _normalize(lhs_value, rhs_value, key=environment_key)
             groups[-1].append(_eval_op(lhs_value, op, rhs_value))
         else:
             assert marker in ["and", "or"]
diff --git a/tests/test_markers.py b/tests/test_markers.py
index 0a16ff277..b1ccf63c6 100644
--- a/tests/test_markers.py
+++ b/tests/test_markers.py
@@ -292,6 +292,14 @@ def test_extra_with_no_extra_in_environment(self):
             ),
             ("extra == 'security'", {"extra": "quux"}, False),
             ("extra == 'security'", {"extra": "security"}, True),
+            ("extra == 'SECURITY'", {"extra": "security"}, True),
+            ("extra == 'security'", {"extra": "SECURITY"}, True),
+            ("extra == 'pep-685-norm'", {"extra": "PEP_685...norm"}, True),
+            (
+                "extra == 'Different.punctuation..is...equal'",
+                {"extra": "different__punctuation_is_EQUAL"},
+                True,
+            ),
         ],
     )
     def test_evaluates(self, marker_string, environment, expected):