diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index f4fea9e2..49c32231 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -25,6 +25,7 @@ jobs:
           - "3.10"
           - "3.11"
           - "3.12"
+          - "3.13"
         toxenv: [py]
         include:
           - python-version: "3.9"
@@ -79,6 +80,7 @@ jobs:
         uses: actions/setup-python@v5
         with:
           python-version: "${{ matrix.python-version }}"
+          allow-prereleases: true
 
       - name: Pip cache
         uses: actions/cache@v4
diff --git a/linkcheck/configuration/__init__.py b/linkcheck/configuration/__init__.py
index e61e78ea..a3213901 100644
--- a/linkcheck/configuration/__init__.py
+++ b/linkcheck/configuration/__init__.py
@@ -386,8 +386,8 @@ def get_user_config():
     )
     if not os.path.exists(userconf):
         # initial config (with all options explained)
-        with importlib.resources.as_file(importlib.resources.files(
-                f"{PACKAGE_NAME}.data").joinpath("linkcheckerrc")) as initialconf:
+        with importlib.resources.path(
+                f"{PACKAGE_NAME}.data", "linkcheckerrc") as initialconf:
             # copy the initial configuration to the user configuration
             try:
                 make_userdir(userconf)
diff --git a/pyproject.toml b/pyproject.toml
index caee384a..2d691123 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -15,6 +15,7 @@ classifiers = [
     "Programming Language :: Python :: 3.10",
     "Programming Language :: Python :: 3.11",
     "Programming Language :: Python :: 3.12",
+    "Programming Language :: Python :: 3.13",
 ]
 
 requires-python = ">=3.9"
diff --git a/tests/checker/data/file-octet-stream.markdown b/tests/checker/data/file-octet-stream.markdown
new file mode 100644
index 00000000..105c84db
--- /dev/null
+++ b/tests/checker/data/file-octet-stream.markdown
@@ -0,0 +1,18 @@
+# Test #
+
+<http://url.example.com>  text <http://url2.example.com>
+
+[link](     http://urllink.example.com)
+
+[link2](http://urllink2
+  .example.com)
+
+[test][id1]
+[URL][id2]
+
+[id1]:       
+http://urldef1.example.com
+
+[id2]: http://urldef2.example.com "URL"
+
+![img](http://urlimg.example.com)
diff --git a/tests/checker/data/file-octet-stream.markdown.result b/tests/checker/data/file-octet-stream.markdown.result
new file mode 100644
index 00000000..5ef8cf67
--- /dev/null
+++ b/tests/checker/data/file-octet-stream.markdown.result
@@ -0,0 +1,42 @@
+url file://%(curdir)s/%(datadir)s/file-octet-stream.markdown
+cache key file://%(curdir)s/%(datadir)s/file-octet-stream.markdown
+real url file://%(curdir)s/%(datadir)s/file-octet-stream.markdown
+name %(datadir)s/file-octet-stream.markdown
+warning The URL with content type 'application/octet-stream' is not parseable.
+valid
+
+url http://url.example.com
+cache key http://url.example.com
+real url http://url.example.com
+error
+
+url http://url2.example.com
+cache key http://url2.example.com
+real url http://url2.example.com
+error
+
+url http://urldef1.example.com
+cache key http://urldef1.example.com
+real url http://urldef1.example.com
+error
+
+url http://urldef2.example.com
+cache key http://urldef2.example.com
+real url http://urldef2.example.com
+error
+
+url http://urllink.example.com
+cache key http://urllink.example.com
+real url http://urllink.example.com
+error
+
+url http://urllink2.example.com
+cache key http://urllink2.example.com
+real url http://urllink2.example.com
+error
+
+url http://urlimg.example.com
+cache key http://urlimg.example.com
+real url http://urlimg.example.com
+error
+
diff --git a/tests/checker/data/file.markdown.result b/tests/checker/data/file.markdown.result
index 3909cc4e..e5a2c90e 100644
--- a/tests/checker/data/file.markdown.result
+++ b/tests/checker/data/file.markdown.result
@@ -2,7 +2,7 @@ url file://%(curdir)s/%(datadir)s/file.markdown
 cache key file://%(curdir)s/%(datadir)s/file.markdown
 real url file://%(curdir)s/%(datadir)s/file.markdown
 name %(datadir)s/file.markdown
-warning The URL with content type 'application/octet-stream' is not parseable.
+warning The URL with content type 'text/markdown' is not parseable.
 valid
 
 url http://url.example.com
diff --git a/tests/checker/test_file.py b/tests/checker/test_file.py
index 81b53f16..b8098d63 100644
--- a/tests/checker/test_file.py
+++ b/tests/checker/test_file.py
@@ -87,7 +87,11 @@ class TestFile(LinkCheckTest):
 
     def test_markdown(self):
         confargs = dict(enabledplugins=["MarkdownCheck"])
-        self.file_test("file.markdown", confargs=confargs)
+        if sys.version_info < (3, 12, 5):
+            markdown_file = "file-octet-stream.markdown"
+        else:
+            markdown_file = "file.markdown"
+        self.file_test(markdown_file, confargs=confargs)
 
     def test_urllist(self):
         self.file_test("urllist.txt")
diff --git a/tox.ini b/tox.ini
index cd7ba097..2878d082 100644
--- a/tox.ini
+++ b/tox.ini
@@ -1,5 +1,5 @@
 [tox]
-envlist = py3{9,10,11,12}, minreqs
+envlist = py3{9,10,11,12,13}, minreqs
 
 [base]
 deps =