diff --git a/.github/workflows/wheel-builder.yml b/.github/workflows/wheel-builder.yml
index 1adb7cf2469b..b4936b42a92f 100644
--- a/.github/workflows/wheel-builder.yml
+++ b/.github/workflows/wheel-builder.yml
@@ -21,6 +21,13 @@ jobs:
           - { NAME: "manylinux2010_x86_64", CONTAINER: "cryptography-manylinux2010:x86_64" }
           - { NAME: "manylinux2014_x86_64", CONTAINER: "cryptography-manylinux2014:x86_64" }
           - { name: "manylinux_2_24_x86_64", CONTAINER: "cryptography-manylinux_2_24:x86_64"}
+          - { name: "musllinux_1_1_x86_64", CONTAINER: "cryptography-musllinux_1_1:x86_64"}
+        exclude:
+          # There are no readily available musllinux PyPy distributions
+          - PYTHON: { VERSION: "pypy3.6", PATH: "/opt/pypy3.6/bin/pypy" }
+            MANYLINUX: { name: "musllinux_1_1_x86_64", CONTAINER: "cryptography-musllinux_1_1:x86_64" }
+          - PYTHON: { VERSION: "pypy3.7", PATH: "/opt/pypy3.7/bin/pypy" }
+            MANYLINUX: { name: "musllinux_1_1_x86_64", CONTAINER: "cryptography-musllinux_1_1:x86_64"}
     name: "${{ matrix.PYTHON.VERSION }} for ${{ matrix.MANYLINUX.NAME }}"
     steps:
       - run: ${{ matrix.PYTHON.PATH }} -m venv .venv
@@ -41,8 +48,8 @@ jobs:
       - run: auditwheel repair --plat ${{ matrix.MANYLINUX.NAME }} tmpwheelhouse/cryptograph*.whl -w wheelhouse/
       - run: unzip wheelhouse/*.whl -d execstack.check
       - run: |
-          results=$(execstack execstack.check/cryptography/hazmat/bindings/*.so)
-          count=$(echo "$results" | grep -c '^X' || true)
+          results=$(readelf -lW execstack.check/cryptography/hazmat/bindings/*.so)
+          count=$(echo "$results" | grep -c 'GNU_STACK.*[R ][W ]E' || true)
           if [ "$count" -ne 0 ]; then
             exit 1
           else