Response　spectrum　analysis　(RSA)　has　been　applied　to　dynamic　calculation　of　underground　structure　subjected　to　earthquake　excitation.　An　analysis　model　composed　of　the　underground　structure　and　the　surrounding　soil　was　built　to　consider　the　soil-structure　interaction　(SSI).　The　seismic　free　field　motion　was　enforced　on　the　bottom　boundary　of　the　calculation　model,　namely　the　inertia　force　acts　on　the　SSI　model　with　fixed　bottom　to　calculate　the　relative　response　of　system.　While　the　scattered　waves　propagating　from　the　model　into　truncated　infinite　domain,　namely　the　radiation　damping　effect　of　infinite　domain,　was　not　considered　in　the　SSI　model.　In　this　paper,　the　viscous-spring　artificial　boundary　(VSAB)　is　used　at　the　bottom　boundary　of　the　SSI　model　to　consider　the　radiation　damping　effect　and　to　improve　the　calculation　accuracy　of　the　model.　The　damping　of　VSAB　makes　the　SSI　model　being　a　non-classically　damping　system.　The　seismic　free　field　is　inputted　as　the　nodal　force　at　VSAB　besides　the　inertia　force　on　SSI　model.　A　generalized　response　spectrum　is　defined　as　the　peak　value　response　of　a　single-degree-of-freedom　(SDOF)　system　subjected　to　the　additional　nodal　force.　Subsequently,　the　complex　modal　RSA　is　generalized　to　calculate　the　seismic　analysis　model　with　VSAB.　Finally,　the　rationality　of　the　generalized　RSA　is　indicated　by　applying　it　to　the　seismic　analysis　of　a　rectangular　subway　station　structure　and　a　circle　tunnel　in　two　typical　sites.　©　2020