To　evaluate　the　seismic　behavior　and　damage　of　bridge　structures　subjected　to　strong　ground　motion　with　reliable　accuracy,　analysis　model　is　generally　recommended.　For　lifeline　structures,　highway　bridges,　it　is　essential　that　residual　displacement　after　an　earthquake　be　smaller　than　the　acceptable　maximum　value　so　that　the　bridges　can　be　repaired.　Both　the　maximum　displacement　and　the　residual　displacement　are　important　in　seismic　design.　Damage　indices　available　in　the　literature,　either　based　on　ductility,　energy　dissipation　or　a　combination　of　both　are　discussed.　The　concept　of　residual　deformation　as　a　critical　complementary　indicator　to　cumulative　damage　is　introduced　in　the　paper.　This　paper　describes　analyses　of　a　typical　bridge,　with　different　hysteretic　characteristics,　post-yielding　stiffness　as　affect　by　P-Delta　effects,　as　well　as　maximum　ductility　are　found　to　influent　residual　deformations　greatly.　Some　important　problems　are　discussed.