Over twenty inscriptions are listed in the Rundata catalog as being signed by Åsmund including U 301 in Skånela, the now-lost U 346 in Frösunda, U 356 in Ängby, the now-lost U 368 in Helgåby, U 824 in Holm, U 847 in Västeråker, U 859 in Måsta, U 871 in Ölsta, U 884 in Ingla, U 932 at Uppsala Cathedral, U 956 in Vedyxa, U 969 in Bolsta, the now-lost U 986 in Kungsgården, U 998 in Skällerö, U 1142 in Åbyggeby, U 1144 in Tierp, U 1149 in Fleräng, U Fv1986;84 in Bo gård, U Fv1988;241 in Rosersberg, Gs 11 in Järvsta, Gs 12 in Lund, and Gs 13 in Söderby.
In the context of Swedish archaeological findings, Åsmund's name is linked to over twenty inscriptions recorded in the Rundata catalog, which include notable examples such as U 301 from Skånela and U 932 at Uppsala Cathedral.