diff --git a/t/t5004-archive-corner-cases.sh b/t/t5004-archive-corner-cases.sh
index cca23383c5..5c886fa823 100755
--- a/t/t5004-archive-corner-cases.sh
+++ b/t/t5004-archive-corner-cases.sh
@@ -155,4 +155,49 @@ test_expect_success ZIPINFO 'zip archive with many entries' '
 	test_cmp expect actual
 '
 
+test_expect_failure EXPENSIVE,UNZIP 'zip archive bigger than 4GB' '
+	# build string containing 65536 characters
+	s=0123456789abcdef0123456789abcdef0123456789abcdef0123456789abcdef &&
+	s=$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s &&
+	s=$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s$s &&
+
+	# create blob with a length of 65536 + 1 bytes
+	blob=$(echo $s | git hash-object -w --stdin) &&
+
+	# create tree containing 65500 entries of that blob
+	for i in $(test_seq 1 65500)
+	do
+		echo "100644 blob $blob	$i"
+	done >tree &&
+	tree=$(git mktree <tree) &&
+
+	# zip it, creating an archive a bit bigger than 4GB
+	git archive -0 -o many-big.zip $tree &&
+
+	"$GIT_UNZIP" -t many-big.zip 9999 65500 &&
+	"$GIT_UNZIP" -t many-big.zip
+'
+
+test_expect_failure EXPENSIVE,UNZIP,ZIPINFO 'zip archive with files bigger than 4GB' '
+	# Pack created with:
+	#   dd if=/dev/zero of=file bs=1M count=4100 && git hash-object -w file
+	mkdir -p .git/objects/pack &&
+	(
+		cd .git/objects/pack &&
+		"$GIT_UNZIP" "$TEST_DIRECTORY"/t5004/big-pack.zip
+	) &&
+	blob=754a93d6fada4c6873360e6cb4b209132271ab0e &&
+	size=$(expr 4100 "*" 1024 "*" 1024) &&
+
+	# create a tree containing the file
+	tree=$(echo "100644 blob $blob	big-file" | git mktree) &&
+
+	# zip it, creating an archive with a file bigger than 4GB
+	git archive -o big.zip $tree &&
+
+	"$GIT_UNZIP" -t big.zip &&
+	"$ZIPINFO" big.zip >big.lst &&
+	grep $size big.lst
+'
+
 test_done
diff --git a/t/t5004/big-pack.zip b/t/t5004/big-pack.zip
new file mode 100644
index 0000000000..caaf614eee
Binary files /dev/null and b/t/t5004/big-pack.zip differ