diff --git a/.github/workflows/wheels.yml b/.github/workflows/wheels.yml
index e9bc52f90..4ed0f5876 100644
--- a/.github/workflows/wheels.yml
+++ b/.github/workflows/wheels.yml
@@ -43,7 +43,7 @@ jobs:
       #     platforms: all
 
       - name: Build wheels
-        uses: pypa/cibuildwheel@v3.0.1
+        uses: pypa/cibuildwheel@v3.1.0
         env:
           CIBW_BUILD: ${{ matrix.build }}
           CIBW_MANYLINUX_X86_64_IMAGE: quay.io/pypa/${{ matrix.image }}
@@ -103,7 +103,7 @@ jobs:
           ref: ${{ github.event.client_payload.ref }}
 
       - name: Build wheels
-        uses: pypa/cibuildwheel@v3.0.1
+        uses: pypa/cibuildwheel@v3.1.0
 
       - uses: actions/upload-artifact@v4
         with:
diff --git a/cibw-requirements.txt b/cibw-requirements.txt
index 0e314b8bf..7e45ab550 100644
--- a/cibw-requirements.txt
+++ b/cibw-requirements.txt
@@ -1 +1 @@
-cibuildwheel==2.23.3
+cibuildwheel==3.1.0
diff --git a/pyproject.toml b/pyproject.toml
index 75d4b91c0..8c74e2960 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -24,7 +24,9 @@ test-extras = "deps"
 build-verbosity = 1
 environment = { CWLTOOL_USE_MYPYC="1", MYPYPATH="$(pwd)/mypy-stubs" }
 # Disable building PyPy wheels on all platforms
-skip = "pp*"
+# Skip free-threaded builds, as mypyc does not support them yet
+# https://mypy.readthedocs.io/en/stable/changelog.html#mypyc-partial-unsafe-support-for-free-threading
+skip = ["pp*", "cp31?t-*"]
 
 # Install system library
 [tool.cibuildwheel.linux]