The　change　of　modal　characteristics　directly　provides　an　indication　of　structural　damage.　Based　on　changes　in　frequencies　and　mode　shapes　of　vibration,　a　damage　identification　technique　is　proposed　in　this　paper　for　predicting　damage　location　and　severity.　The　method　is　applied　at　an　element　level　with　a　conventional　finite-element　model.　The　element　damage　equations　have　been　established　through　the　eigenvalue　equations　that　characterize　the　dynamic　behavior.　Several　solution　techniques　are　discussed　and　compared.　The　influence　of　simulated　noise　in　the　modal　data　is　also　presented.　The　method　has　been　verified　by　a　number　of　damage　scenarios　for　simulated　beams　and　has　found　the　exact　location　and　severity　of　damage.　It　is　demonstrated　that　multiplying　the　damaged　eigenvalue　equations　with　the　undamaged　or　damaged　mode　shapes　provides　more　equations　and　guarantees　the　damage　localization.　The　resulting　equations,　however,　become　more　sensitive　to　the　deviation　of　modal　data　and　the　direct　solution　often　yields　poor　results.　Numerical　results　show　that　the　non-negative　least-squares　method　can　lead　to　satisfactory　results　in　most　cases.　A　regularization　algorithm　with　error-based　truncation　is　necessary　to　ensure　the　right　solutions.