diff --git a/var/spack/repos/builtin/packages/udunits/package.py b/var/spack/repos/builtin/packages/udunits/package.py
index 2b92c71d472c78..f63c00a9973dfd 100644
--- a/var/spack/repos/builtin/packages/udunits/package.py
+++ b/var/spack/repos/builtin/packages/udunits/package.py
@@ -35,10 +35,24 @@ class Udunits(AutotoolsPackage):
     depends_on("expat")
 
     variant("shared", default=True, description="Build shared library")
+    variant(
+        "pic",
+        default=True,
+        description="Enable position-independent code (PIC)",
+        when="~shared",
+    )
 
     @property
     def libs(self):
-        return find_libraries(["libudunits2"], root=self.prefix, recursive=True, shared=True)
+        return find_libraries(
+            "libudunits2",
+            root=self.prefix,
+            recursive=True,
+            shared=self.spec.satisfies("+shared")
+        )
 
     def configure_args(self):
-        return self.enable_or_disable("shared")
+        config_args = []
+        config_args.extend(self.enable_or_disable("shared"))
+        config_args.extend(self.with_or_without("pic"))
+        return config_args