diff --git a/elf/Makefile b/elf/Makefile
index 838fe39afb..f141eedfb0 100644
--- a/elf/Makefile
+++ b/elf/Makefile
@@ -466,6 +466,7 @@ tests += \
   tst-unique2 \
   tst-unwind-ctor \
   tst-unwind-main \
+  tst-version-hash-zero \
   unload3 \
   unload4 \
   unload5 \
@@ -913,6 +914,9 @@ modules-names += \
   tst-unique2mod1 \
   tst-unique2mod2 \
   tst-unwind-ctor-lib \
+  tst-version-hash-zero-linkmod \
+  tst-version-hash-zero-mod \
+  tst-version-hash-zero-refmod \
   unload2dep \
   unload2mod \
   unload3mod1 \
@@ -2960,3 +2964,25 @@ $(objpfx)tst-tls-allocation-failure-static-patched.out: \
 	grep -q '^Fatal glibc error: Cannot allocate TLS block$$' $@ \
 	  && grep -q '^status: 127$$' $@; \
 	  $(evaluate-test)
+
+$(objpfx)tst-version-hash-zero.out: \
+  $(objpfx)tst-version-hash-zero-mod.so \
+  $(objpfx)tst-version-hash-zero-refmod.so
+$(objpfx)tst-version-hash-zero-mod.so: $(objpfx)tst-version-hash-zero-mod.os \
+  tst-version-hash-zero-mod.map
+	$(LINK.o) -shared -o $@ $(LDFLAGS.so) $< \
+	  -Wl,--version-script=tst-version-hash-zero-mod.map
+# The run-time test module tst-version-hash-zero-refmod.so is linked
+# to a stub module, tst-version-hash-zero-linkmod.so, to produce an
+# expected relocation error.
+$(objpfx)tst-version-hash-zero-refmod.so: \
+  $(objpfx)tst-version-hash-zero-linkmod.so
+$(objpfx)tst-version-hash-zero-linkmod.so:\
+  $(objpfx)tst-version-hash-zero-linkmod.os \
+  tst-version-hash-zero-linkmod.map
+	$(LINK.o) -shared -o $@ $(LDFLAGS.so) $< \
+	  -Wl,--version-script=tst-version-hash-zero-linkmod.map \
+	  -Wl,--soname=tst-version-hash-zero-mod.so
+$(objpfx)tst-version-hash-zero-refmod.so: \
+  $(objpfx)tst-version-hash-zero-linkmod.so
+tst-version-hash-zero-refmod.so-no-z-defs = yes
diff --git a/elf/dl-lookup.c b/elf/dl-lookup.c
index a42f6d5390..9abe96fd92 100644
--- a/elf/dl-lookup.c
+++ b/elf/dl-lookup.c
@@ -114,12 +114,22 @@ check_match (const char *const undef_name,
 	  /* We can match the version information or use the
 	     default one if it is not hidden.  */
 	  ElfW(Half) ndx = verstab[symidx] & 0x7fff;
-	  if ((map->l_versions[ndx].hash != version->hash
-	       || strcmp (map->l_versions[ndx].name, version->name))
-	      && (version->hidden || map->l_versions[ndx].hash
-		  || (verstab[symidx] & 0x8000)))
-	    /* It's not the version we want.  */
-	    return NULL;
+	  if (map->l_versions[ndx].hash == version->hash
+	      && strcmp (map->l_versions[ndx].name, version->name) == 0)
+	    /* This is an exact version match.  Return the symbol below.  */
+	    ;
+	  else
+	    {
+	      if (!version->hidden
+		  && map->l_versions[ndx].name[0] == '\0'
+		  && (verstab[symidx] & 0x8000) == 0
+		  && (*num_versions)++ == 0)
+		/* This is the global default version.  Store it as a
+		   fallback match.  */
+		*versioned_sym = sym;
+
+	      return NULL;
+	    }
 	}
     }
   else
diff --git a/elf/dl-version.c b/elf/dl-version.c
index cda0889209..c10ead82fe 100644
--- a/elf/dl-version.c
+++ b/elf/dl-version.c
@@ -357,6 +357,13 @@ _dl_check_map_versions (struct link_map *map, int verbose, int trace_mode)
 	      ent = (ElfW(Verdef) *) ((char *) ent + ent->vd_next);
 	    }
 	}
+
+      /* The empty string has ELF hash zero.  This avoids a NULL check
+	 before the version string comparison in check_match in
+	 dl-lookup.c.  */
+      for (unsigned int i = 0; i < map->l_nversions; ++i)
+	if (map->l_versions[i].name == NULL)
+	  map->l_versions[i].name = "";
     }
 
   /* When there is a DT_VERNEED entry with libc.so on DT_NEEDED, issue
diff --git a/elf/tst-version-hash-zero-linkmod.c b/elf/tst-version-hash-zero-linkmod.c
new file mode 100644
index 0000000000..f71574bd2d
--- /dev/null
+++ b/elf/tst-version-hash-zero-linkmod.c
@@ -0,0 +1,22 @@
+/* Stub module for linking tst-version-hash-zero-refmod.so.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public License as
+   published by the Free Software Foundation; either version 2.1 of the
+   License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; see the file COPYING.LIB.  If
+   not, see <https://www.gnu.org/licenses/>.  */
+
+/* The version script assigns a different symbol version for the stub
+   module.  Loading the module with the incorrect version is expected
+   to fail.  */
+#include "tst-version-hash-zero-mod.c"
diff --git a/elf/tst-version-hash-zero-linkmod.map b/elf/tst-version-hash-zero-linkmod.map
new file mode 100644
index 0000000000..2dba7c22d7
--- /dev/null
+++ b/elf/tst-version-hash-zero-linkmod.map
@@ -0,0 +1,7 @@
+Base {
+  local: *;
+};
+
+OTHER_VERSION {
+  global: global_variable;
+} Base;
diff --git a/elf/tst-version-hash-zero-mod.c b/elf/tst-version-hash-zero-mod.c
new file mode 100644
index 0000000000..f99c020746
--- /dev/null
+++ b/elf/tst-version-hash-zero-mod.c
@@ -0,0 +1,20 @@
+/* Test module with a zero version symbol hash.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public License as
+   published by the Free Software Foundation; either version 2.1 of the
+   License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; see the file COPYING.LIB.  If
+   not, see <https://www.gnu.org/licenses/>.  */
+
+/* The symbol version is assigned by version script.  */
+int global_variable;
diff --git a/elf/tst-version-hash-zero-mod.map b/elf/tst-version-hash-zero-mod.map
new file mode 100644
index 0000000000..41eaff7914
--- /dev/null
+++ b/elf/tst-version-hash-zero-mod.map
@@ -0,0 +1,13 @@
+Base {
+  local: *;
+};
+
+/* Define the version so that tst-version-hash-zero-refmod.so passes
+   the initial symbol version check.  */
+OTHER_VERSION {
+} Base;
+
+/* This version string hashes to zero.  */
+PPPPPPPPPPPP {
+  global: global_variable;
+} Base;
diff --git a/elf/tst-version-hash-zero-refmod.c b/elf/tst-version-hash-zero-refmod.c
new file mode 100644
index 0000000000..29a9caaa40
--- /dev/null
+++ b/elf/tst-version-hash-zero-refmod.c
@@ -0,0 +1,23 @@
+/* Test module that triggers a relocation failure in tst-version-hash-zero.
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public License as
+   published by the Free Software Foundation; either version 2.1 of the
+   License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; see the file COPYING.LIB.  If
+   not, see <https://www.gnu.org/licenses/>.  */
+
+/* This is bound to global_variable@@OTHER_VERSION via
+   tst-version-hash-zero-linkmod.so, but at run time, only
+   global_variable@PPPPPPPPPPPP exists.  */
+extern int global_variable;
+int *pointer_variable = &global_variable;
diff --git a/elf/tst-version-hash-zero.c b/elf/tst-version-hash-zero.c
new file mode 100644
index 0000000000..ad391bf202
--- /dev/null
+++ b/elf/tst-version-hash-zero.c
@@ -0,0 +1,55 @@
+/* Symbols with version hash zero should not match any version (bug 29190).
+   Copyright (C) 2022 Free Software Foundation, Inc.
+   This file is part of the GNU C Library.
+
+   The GNU C Library is free software; you can redistribute it and/or
+   modify it under the terms of the GNU Lesser General Public License as
+   published by the Free Software Foundation; either version 2.1 of the
+   License, or (at your option) any later version.
+
+   The GNU C Library is distributed in the hope that it will be useful,
+   but WITHOUT ANY WARRANTY; without even the implied warranty of
+   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
+   Lesser General Public License for more details.
+
+   You should have received a copy of the GNU Lesser General Public
+   License along with the GNU C Library; see the file COPYING.LIB.  If
+   not, see <https://www.gnu.org/licenses/>.  */
+
+#include <support/check.h>
+#include <support/xdlfcn.h>
+#include <stddef.h>
+#include <string.h>
+
+static int
+do_test (void)
+{
+  void *handle = xdlopen ("tst-version-hash-zero-mod.so", RTLD_NOW);
+
+  /* This used to crash because some struct r_found_version entries
+     with hash zero did not have valid version strings.  */
+  TEST_VERIFY (xdlvsym (handle, "global_variable", "PPPPPPPPPPPP") != NULL);
+
+  /* Consistency check.  */
+  TEST_VERIFY (xdlsym (handle, "global_variable")
+               == xdlvsym (handle, "global_variable", "PPPPPPPPPPPP"));
+
+  /* This symbol version is supposed to be missing.  */
+  TEST_VERIFY (dlvsym (handle, "global_variable", "OTHER_VERSION") == NULL);
+
+  /* tst-version-hash-zero-refmod.so references
+     global_variable@@OTHER_VERSION and is expected to fail to load.
+     dlvsym sets the hidden flag during lookup.  Relocation does not,
+     so this exercises a different failure case.  */
+  TEST_VERIFY (dlopen ("tst-version-hash-zero-refmod.so", RTLD_NOW) == NULL);
+  const char *message = dlerror ();
+  if (strstr (message,
+              ": undefined symbol: global_variable, version OTHER_VERSION")
+      == NULL)
+    FAIL_EXIT1 ("unexpected dlopen failure: %s", message);
+
+  xdlclose (handle);
+  return 0;
+}
+
+#include <support/test-driver.c>
