High　Strength　Structural　(HSS)　steels,　with　nominal　yield　strength　not　less　than　460　MPa　are　rapidly　gaining　popularity　in　steel　construction　worldwide.　These　steels　exhibit　phenomena,　such　as　the　Lode　angle　dependence　of　yield　and　accelerated　cyclic　softening　at　large　accumulated　plastic　strains,　which　cannot　be　conveniently　simulated　by　existing　constitutive　models　that　are　developed　primarily　for　normal　strength　structural　steels.　Moreover,　in　the　area　of　steel　structures,　the　failure　location　of　steel　members　is　generally　undergoing　large　plastic　deformation　at　triaxial　stress　states.　In　order　to　describe　and　predict　cyclic　behavior　of　HSS　steels　under　multi-axis　stress　states,　a　new　cyclic　constitutive　model　with　the　consideration　of　accumulative　damage　and　the　influence　of　triaxial　stress　states　based　on　ductile　fracture　model　is　formulated　to　simulate　the　response　of　HSS　steels　subjected　to　a　range　of　loading　types　in　terms　of　triaxial　stress　state　and　loading　histories.　The　proposed　model,　termed　as　HSS-3D,　is　calibrited　by　experimental　results　consisting　of　coupon　scale　monotonic　and　cyclic　tests.　It　is　determined　that　the　HSS-3D　model　shows　significant　improvement　in　accuracy　for　HSS　steels　compared　to　the　commonly　used　Armstrong　Frederick　model.　The　proposed　HSS-3D　model　is　able　to　simulate:　(1)　the　Lode　angle　dependence　through　an　enhanced　yield　function　which　modifies　the　conventional　von　Mises　yield　surface;　(2)　the　deterioration　of　the　elastic　region　at　high　accumulated　strains　through　new　isotropic　softening　relationship;　(3)　the　influence　of　stress　states　on　strength　softening　behavior　of　HSS　steels　and　(4)　ductile　fracture　of　steels　under　cyclic　loading.　©　2022　the　Author(s).