diff --git a/fix-big-endian-build.patch b/fix-big-endian-build.patch
new file mode 100644
index 0000000..2eaa482
--- /dev/null
+++ b/fix-big-endian-build.patch
@@ -0,0 +1,57 @@
+From efb42e3a40c4e1ea043902b0ac989af9af5dedbb Mon Sep 17 00:00:00 2001
+From: Tzu-ping Chung <uranusjr@gmail.com>
+Date: Wed, 20 Apr 2022 10:00:07 +0800
+Subject: [PATCH] Correctly parse ELF for musllinux on Big Endian
+
+Always use LSB to parse binary in tests
+---
+ packaging/_musllinux.py | 8 +++++---
+ tests/test_musllinux.py | 9 +++++----
+ 2 files changed, 10 insertions(+), 7 deletions(-)
+
+diff --git a/packaging/_musllinux.py b/packaging/_musllinux.py
+index 8ac3059..d5d3e04 100644
+--- a/packaging/_musllinux.py
++++ b/packaging/_musllinux.py
+@@ -39,9 +39,11 @@ def _parse_ld_musl_from_elf(f: IO[bytes]) -> Optional[str]:
+         # p_fmt: Format for section header.
+         # p_idx: Indexes to find p_type, p_offset, and p_filesz.
+         e_fmt, p_fmt, p_idx = {
+-            1: ("IIIIHHH", "IIIIIIII", (0, 1, 4)),  # 32-bit.
+-            2: ("QQQIHHH", "IIQQQQQQ", (0, 2, 5)),  # 64-bit.
+-        }[ident[4]]
++            (1, 1): ("<IIIIHHH", "<IIIIIIII", (0, 1, 4)),  # 32-bit LSB.
++            (1, 2): (">IIIIHHH", ">IIIIIIII", (0, 1, 4)),  # 32-bit MSB.
++            (2, 1): ("<QQQIHHH", "<IIQQQQQQ", (0, 2, 5)),  # 64-bit LSB.
++            (2, 2): (">QQQIHHH", ">IIQQQQQQ", (0, 2, 5)),  # 64-bit MSB.
++        }[(ident[4], ident[5])]
+     except KeyError:
+         return None
+     else:
+diff --git a/tests/test_musllinux.py b/tests/test_musllinux.py
+index d2c87ca..2623bdb 100644
+--- a/tests/test_musllinux.py
++++ b/tests/test_musllinux.py
+@@ -101,14 +101,15 @@ def test_parse_ld_musl_from_elf_no_interpreter_section():
+     with BIN_MUSL_X86_64.open("rb") as f:
+         data = f.read()
+ 
+-    # Change all sections to *not* PT_INTERP.
+-    unpacked = struct.unpack("16BHHIQQQIHHH", data[:58])
++    # Change all sections to *not* PT_INTERP. We are explicitly using LSB rules
++    # because the binaries are in LSB.
++    unpacked = struct.unpack("<16BHHIQQQIHHH", data[:58])
+     *_, e_phoff, _, _, _, e_phentsize, e_phnum = unpacked
+     for i in range(e_phnum + 1):
+         sb = e_phoff + e_phentsize * i
+         se = sb + 56
+-        section = struct.unpack("IIQQQQQQ", data[sb:se])
+-        data = data[:sb] + struct.pack("IIQQQQQQ", 0, *section[1:]) + data[se:]
++        section = struct.unpack("<IIQQQQQQ", data[sb:se])
++        data = data[:sb] + struct.pack("<IIQQQQQQ", 0, *section[1:]) + data[se:]
+ 
+     assert _parse_ld_musl_from_elf(io.BytesIO(data)) is None
+ 
+-- 
+2.36.1
+
diff --git a/python-packaging.changes b/python-packaging.changes
index 63879b7..6219fbc 100644
--- a/python-packaging.changes
+++ b/python-packaging.changes
@@ -1,3 +1,9 @@
+-------------------------------------------------------------------
+Sun May 29 09:22:42 UTC 2022 - John Paul Adrian Glaubitz <adrian.glaubitz@suse.com>
+
+- Add patch to fix testsuite on big-endian targets
+  + fix-big-endian-build.patch
+
 -------------------------------------------------------------------
 Mon Apr 25 07:56:29 UTC 2022 - Hui-Zhi Zhao <hui.zhi.zhao@suse.com>
 
diff --git a/python-packaging.spec b/python-packaging.spec
index f9459b2..08b66b2 100644
--- a/python-packaging.spec
+++ b/python-packaging.spec
@@ -37,6 +37,9 @@ URL:            https://github.com/pypa/packaging
 Source:         https://files.pythonhosted.org/packages/source/p/packaging/packaging-%{version}.tar.gz
 # Restore compatibility with 20.4 for setuptools
 Patch1:         no-legacyversion-warning.patch
+# Fix testsuite on big-endian systems
+# see: https://github.com/pypa/packaging/pull/538
+Patch2:         fix-big-endian-build.patch
 BuildRequires:  %{python_module devel}
 BuildRequires:  fdupes
 BuildRequires:  python-rpm-macros