diff --git a/.github/workflows/tests.yml b/.github/workflows/tests.yml
index 634c83fa57fd..cd4c08e29fb9 100644
--- a/.github/workflows/tests.yml
+++ b/.github/workflows/tests.yml
@@ -88,14 +88,31 @@ jobs:
             pyqt6-ver: '!=6.6.0'
             # https://bugreports.qt.io/projects/PYSIDE/issues/PYSIDE-2346
             pyside6-ver: '!=6.5.1'
-          - os: macos-12  # This runnre is on Intel chips.
-            python-version: 3.9
+          - os: ubuntu-22.04
+            python-version: '3.13'
+            # https://www.riverbankcomputing.com/pipermail/pyqt/2023-November/045606.html
+            pyqt6-ver: '!=6.6.0'
+            # https://bugreports.qt.io/projects/PYSIDE/issues/PYSIDE-2346
+            pyside6-ver: '!=6.5.1'
+          - name-suffix: "Free-threaded"
+            os: ubuntu-22.04
+            python-version: '3.13t'
+            # https://www.riverbankcomputing.com/pipermail/pyqt/2023-November/045606.html
+            pyqt6-ver: '!=6.6.0'
+            # https://bugreports.qt.io/projects/PYSIDE/issues/PYSIDE-2346
+            pyside6-ver: '!=6.5.1'
+          - os: macos-12  # This runner is on Intel chips.
+            python-version: '3.9'
             # https://bugreports.qt.io/projects/PYSIDE/issues/PYSIDE-2346
             pyside6-ver: '!=6.5.1'
           - os: macos-14  # This runner is on M1 (arm64) chips.
             python-version: '3.12'
             # https://bugreports.qt.io/projects/PYSIDE/issues/PYSIDE-2346
             pyside6-ver: '!=6.5.1'
+          - os: macos-14  # This runner is on M1 (arm64) chips.
+            python-version: '3.13'
+            # https://bugreports.qt.io/projects/PYSIDE/issues/PYSIDE-2346
+            pyside6-ver: '!=6.5.1'
 
     steps:
       - uses: actions/checkout@v4
@@ -104,8 +121,17 @@ jobs:
 
       - name: Set up Python ${{ matrix.python-version }}
         uses: actions/setup-python@v5
+        if: matrix.python-version != '3.13t'
         with:
           python-version: ${{ matrix.python-version }}
+          allow-prereleases: true
+
+      - name: Set up Python ${{ matrix.python-version }}
+        uses: deadsnakes/action@6c8b9b82fe0b4344f4b98f2775fcc395df45e494  # v3.1.0
+        if: matrix.python-version == '3.13t'
+        with:
+          python-version: '3.13'
+          nogil: true
 
       - name: Install OS dependencies
         run: |
@@ -152,6 +178,11 @@ jobs:
               texlive-luatex \
               texlive-pictures \
               texlive-xetex
+            if [[ "${{ matrix.python-version }}" = '3.13t' ]]; then
+              # TODO: Remove this once setup-python supports nogil distributions.
+              sudo apt-get install -yy --no-install-recommends \
+                python3.13-tk-nogil
+            fi
             if [[ "${{ matrix.os }}" = ubuntu-20.04 ]]; then
               sudo apt-get install -yy --no-install-recommends libopengl0
             else  # ubuntu-22.04
@@ -202,6 +233,15 @@ jobs:
             4-${{ runner.os }}-py${{ matrix.python-version }}-mpl-${{ github.ref }}-
             4-${{ runner.os }}-py${{ matrix.python-version }}-mpl-
 
+      - name: Install the nightly dependencies
+        if: matrix.python-version == '3.13t'
+        run: |
+          python -m pip install pytz tzdata python-dateutil  # Must be installed for Pandas.
+          python -m pip install \
+              --pre \
+              --index-url https://pypi.anaconda.org/scientific-python-nightly-wheels/simple \
+              --upgrade --only-binary=:all: numpy pandas pillow contourpy
+
       - name: Install Python dependencies
         run: |
           # Upgrade pip and setuptools and wheel to get as clean an install as
@@ -227,6 +267,7 @@ jobs:
           # Sphinx is needed to run sphinxext tests
           python -m pip install --upgrade sphinx!=6.1.2
 
+          if [[ "${{ matrix.python-version }}" != '3.13t' ]]; then
           # GUI toolkits are pip-installable only for some versions of Python
           # so don't fail if we can't install them.  Make it easier to check
           # whether the install was successful by trying to import the toolkit
@@ -246,11 +287,11 @@ jobs:
             python -c 'import PyQt5.QtCore' &&
             echo 'PyQt5 is available' ||
             echo 'PyQt5 is not available'
-          # Even though PySide2 wheels can be installed on Python 3.12, they are broken and since PySide2 is
+          # Even though PySide2 wheels can be installed on Python 3.12+, they are broken and since PySide2 is
           # deprecated, they are unlikely to be fixed. For the same deprecation reason, there are no wheels
           # on M1 macOS, so don't bother there either.
           if [[ "${{ matrix.os }}" != 'macos-14'
-                && "${{ matrix.python-version }}" != '3.12' ]]; then
+                && "${{ matrix.python-version }}" != '3.12' && "${{ matrix.python-version }}" != '3.13' ]]; then
             python -mpip install --upgrade pyside2${{ matrix.pyside2-ver }} &&
               python -c 'import PySide2.QtCore' &&
               echo 'PySide2 is available' ||
@@ -272,6 +313,8 @@ jobs:
             echo 'wxPython is available' ||
             echo 'wxPython is not available'
 
+          fi  # Skip backends on Python 3.13t.
+
       - name: Install the nightly dependencies
         # Only install the nightly dependencies during the scheduled event
         if: github.event_name == 'schedule' && matrix.name-suffix != '(Minimum Versions)'
@@ -310,6 +353,9 @@ jobs:
 
       - name: Run pytest
         run: |
+          if [[ "${{ matrix.python-version }}" == '3.13t' ]]; then
+            export PYTHON_GIL=0
+          fi
           pytest -rfEsXR -n auto \
             --maxfail=50 --timeout=300 --durations=25 \
             --cov-report=xml --cov=lib --log-level=DEBUG --color=yes
diff --git a/lib/matplotlib/tests/test_axes.py b/lib/matplotlib/tests/test_axes.py
index 3ec9923c0840..e99ef129eb9a 100644
--- a/lib/matplotlib/tests/test_axes.py
+++ b/lib/matplotlib/tests/test_axes.py
@@ -1186,7 +1186,7 @@ def test_imshow():
 
 @image_comparison(
     ['imshow_clip'], style='mpl20',
-    tol=1.24 if platform.machine() in ('aarch64', 'ppc64le', 's390x') else 0)
+    tol=1.24 if platform.machine() in ('aarch64', 'arm64', 'ppc64le', 's390x') else 0)
 def test_imshow_clip():
     # As originally reported by Gellule Xg <gellule.xg@free.fr>
     # use former defaults to match existing baseline image
@@ -2570,7 +2570,7 @@ def test_contour_hatching():
 
 @image_comparison(
     ['contour_colorbar'], style='mpl20',
-    tol=0.54 if platform.machine() in ('aarch64', 'ppc64le', 's390x') else 0)
+    tol=0.54 if platform.machine() in ('aarch64', 'arm64', 'ppc64le', 's390x') else 0)
 def test_contour_colorbar():
     x, y, z = contour_dat()
 
diff --git a/lib/matplotlib/tests/test_contour.py b/lib/matplotlib/tests/test_contour.py
index d4600a14fe1c..0622c099a20c 100644
--- a/lib/matplotlib/tests/test_contour.py
+++ b/lib/matplotlib/tests/test_contour.py
@@ -442,7 +442,7 @@ def test_contourf_log_extension(split_collections):
 @pytest.mark.parametrize("split_collections", [False, True])
 @image_comparison(
     ['contour_addlines.png'], remove_text=True, style='mpl20',
-    tol=0.15 if platform.machine() in ('aarch64', 'ppc64le', 's390x')
+    tol=0.15 if platform.machine() in ('aarch64', 'arm64', 'ppc64le', 's390x')
         else 0.03)
 # tolerance is because image changed minutely when tick finding on
 # colorbars was cleaned up...
diff --git a/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py b/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
index ecb51b724c27..ff5ab230ef06 100644
--- a/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
+++ b/lib/mpl_toolkits/mplot3d/tests/test_axes3d.py
@@ -221,7 +221,7 @@ def test_bar3d_lightsource():
 
 @mpl3d_image_comparison(
     ['contour3d.png'], style='mpl20',
-    tol=0.002 if platform.machine() in ('aarch64', 'ppc64le', 's390x') else 0)
+    tol=0.002 if platform.machine() in ('aarch64', 'arm64', 'ppc64le', 's390x') else 0)
 def test_contour3d():
     plt.rcParams['axes3d.automargin'] = True  # Remove when image is regenerated
     fig = plt.figure()