diff --git a/.github/workflows/build-wheels.yml b/.github/workflows/build-wheels.yml
index 69f63198c8..0038748980 100644
--- a/.github/workflows/build-wheels.yml
+++ b/.github/workflows/build-wheels.yml
@@ -72,10 +72,10 @@ jobs:
     steps:
       - uses: actions/setup-python@v5
         with:
-          version: 3.12
+          python-version: 3.12
 
       - name: Install Python dependencies
-        run: python -m pip install cibuildwheel simple503 wheel
+        run: python -m pip install cibuildwheel simple503 build
 
       - name: Checkout Basix
         if: ${{ github.event.inputs.build_fenicsx_stack == 'true' }}
@@ -87,8 +87,8 @@ jobs:
 
       - name: Build Basix wheel
         if: ${{ github.event.inputs.build_fenicsx_stack == 'true' }}
+        working-directory: basix
         run: |
-          cd basix
           python -m cibuildwheel --output-dir ../wheelhouse .
 
       - name: Checkout UFL
@@ -101,7 +101,8 @@ jobs:
 
       - name: Build UFL wheel
         if: ${{ github.event.inputs.build_fenicsx_stack == 'true' }}
-        run: python -m pip wheel --no-deps -w wheelhouse ./ufl
+        working-directory: ufl
+        run: python -m build --outdir wheelhouse/ .
 
       - name: Checkout FFCx
         if: ${{ github.event.inputs.build_fenicsx_stack == 'true' }}
@@ -113,7 +114,7 @@ jobs:
 
       - name: Build FFCx wheel
         if: ${{ github.event.inputs.build_fenicsx_stack == 'true' }}
-        run: python -m pip wheel --no-deps -w wheelhouse ./ffcx
+        run: python -m build --outdir wheelhouse/ .
 
       - name: Make temporary simple503 repository
         run: |
@@ -137,7 +138,7 @@ jobs:
       - name: Build DOLFINx wheel
         run: python -m cibuildwheel --output-dir wheelhouse dolfinx/python
         env:
-          CIBW_BEFORE_BUILD: yum -y update && yum -y install mpich && python -m pip -v install --prefer-binary fenics-ffcx fenics-basix fenics-ufl && python -m pip -v install --prefer-binary mpi4py -i https://pypi.anaconda.org/mpi4py/simple && cmake -S dolfinx/cpp -B build-dir -DPython3_EXECUTABLE=$(which python) && cmake --build build-dir && cmake --install build-dir
+          CIBW_BEFORE_BUILD: yum -y update && yum -y install mpich-devel && python -m pip -v install --prefer-binary fenics-ffcx fenics-basix fenics-ufl && python -m pip -v install --prefer-binary mpi4py -i https://pypi.anaconda.org/mpi4py/simple && cmake -S dolfinx/cpp -B build-dir -DPython3_EXECUTABLE=$(which python) && cmake --build build-dir && cmake --install build-dir
           CIBW_REPAIR_WHEEL_COMMAND_LINUX: export LD_LIBRARY_PATH=$(python -c "import site; print(site.getsitepackages()[0] + '/fenics_basix.libs')"):${LD_LIBRARY_PATH} && auditwheel repair -w {dest_dir} {wheel}
           CIBW_ENVIRONMENT: PIP_EXTRA_INDEX_URL=file:///project/simple MAKEFLAGS=-j3 LD_LIBRARY_PATH=/usr/lib64/mpich/lib