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.
Åsmund is associated with numerous inscriptions documented in the Rundata catalog, including those identified by numbers U 301 through U 1149, which were discovered in various sites across Sweden.