diff --git a/Regression/RHEL-79256_annocheck_runs_out_of_file_descriptors/main.fmf b/Regression/RHEL-79256_annocheck_runs_out_of_file_descriptors/main.fmf
new file mode 100644
index 0000000..a9807e8
--- /dev/null
+++ b/Regression/RHEL-79256_annocheck_runs_out_of_file_descriptors/main.fmf
@@ -0,0 +1,29 @@
+summary: Be modest with open files
+contact: Vaclav Kadlcik <vkadlcik@redhat.com>
+component:
+  - annobin
+test: ${WITH_SCL:-bash} ./runtest.sh
+framework: beakerlib
+recommend:
+  - annobin-annocheck
+duration: 20m
+enabled: true
+tag:
+  - CI-Tier-1
+tier: '1'
+link:
+  - relates: https://issues.redhat.com/browse/RHEL-79256
+adjust:
+  - enabled: false
+    when: collection is not defined and distro == rhel-9 and distro ~< rhel-9.6
+    continue: false
+  - enabled: false
+    when: collection is not defined and distro < rhel-9
+    continue: false
+  - enabled: false
+    when: collection == devtoolset-13, gcc-toolset-13, gcc-toolset-14
+    continue: false
+extra-summary: /tools/annobin/Regression/RHEL-79256_annocheck_runs_out_of_file_descriptors
+extra-task: /tools/annobin/Regression/RHEL-79256_annocheck_runs_out_of_file_descriptors
+# extra-nitrate: TODO
+# id: TODO
diff --git a/Regression/RHEL-79256_annocheck_runs_out_of_file_descriptors/runtest.sh b/Regression/RHEL-79256_annocheck_runs_out_of_file_descriptors/runtest.sh
new file mode 100755
index 0000000..62d0314
--- /dev/null
+++ b/Regression/RHEL-79256_annocheck_runs_out_of_file_descriptors/runtest.sh
@@ -0,0 +1,48 @@
+#!/usr/bin/env bash
+. /usr/share/beakerlib/beakerlib.sh || exit 1
+
+ANNOCHECK="${ANNOCHECK:-$(type -P annocheck)}"
+ANNOCHECK_RPM_NAME=$(rpm --qf '%{name}' -qf "$ANNOCHECK")
+
+PACKAGES="$ANNOCHECK_RPM_NAME"
+
+rlJournalStart
+    rlPhaseStartSetup
+        rlLogInfo "PACKAGES=$PACKAGES"
+        rlLogInfo "COLLECTIONS=$COLLECTIONS"
+        rlLogInfo "ANNOCHECK=$ANNOCHECK"
+        rlLogInfo "SKIP_COLLECTION_METAPACKAGE_CHECK=$SKIP_COLLECTION_METAPACKAGE_CHECK"
+
+        # We optionally need to skip checking for the presence of the metapackage
+        # because that would pull in all the dependent toolset subrpms.  We do not
+        # always want that, especially in CI.
+        _COLLECTIONS="$COLLECTIONS"
+        if ! test -z "$SKIP_COLLECTION_METAPACKAGE_CHECK"; then
+            for c in $SKIP_COLLECTION_METAPACKAGE_CHECK; do
+                rlLogInfo "ignoring metapackage check for collection $c"
+                export COLLECTIONS=$(shopt -s extglob && echo ${COLLECTIONS//$c/})
+            done
+        fi
+        rlLogInfo "(without skipped) COLLECTIONS=$COLLECTIONS"
+        rlAssertRpm --all
+        export COLLECTIONS="$_COLLECTIONS"
+
+        rlRun "TmpDir=\$(mktemp -d)"
+        rlRun "pushd $TmpDir"
+    rlPhaseEnd
+
+    rlPhaseStartTest
+        rlRun 'annocheck -n --ignore-links --ignore-unknown --skip-passes --skip-all --test-stack-prot /usr &>annocheck.out' 0,1
+        for i in 'Could not open' 'system error:' 'Too many open files'; do
+            rlAssertNotGrep "$i" annocheck.out
+        done
+        rlAssertGrep '^Final totals' annocheck.out
+        rlGetPhaseState || rlFileSubmit annocheck.out annocheck.out
+    rlPhaseEnd
+
+    rlPhaseStartCleanup
+        rlRun popd
+        rlRun "rm -r $TmpDir"
+    rlPhaseEnd
+rlJournalPrintText
+rlJournalEnd