Due　to　the　sufficient　toughness　and　high　strength,　the　High　Strength　Structural　(HSS)　steels　with　nominal　yield　strength　not　less　than　460　MPa　are　rapidly　gaining　popularity　in　steel　construction　worldwide.　The　failure　point　of　steel　elements　in　steel　structures　typically　experiences　significant　plastic　deformation　at　triaxial　stress　levels.　In　order　to　study　the　ultra-low　cyclic　behavior　of　HSS　steels　at　various　triaxial　stress　states,　a　series　of　cyclic　tests　on　three　typical　HSS　steels　specimens　with　various　initial　geometrics　are　designed　and　conducted　in　the　present　study.　The　characteristics　of　HSS　steels　including　Lode　angle　dependence　of　yield　strength,　combined　hardening　and　three-stage　strength　softening　are　observed.　Moreover,　the　strength　softening　laws　of　HSS　steels　are　different　at　various　stress　states.　However,　the　existing　constitutive　models　fails　to　capture　strength　softening　of　HSS　steels　when　subjected　to　a　range　of　loading　types　in　terms　of　various　triaxial　stress　states.　Based　on　ductile　damage　mechanism,　a　new　cyclic　constitutive　model　(HSS-3D)　with　consideration　of　damage　accumulation　and　influence　of　triaxial　stress　states　is　proposed.　The　HSS-3D　model　is　implemented　into　ABAQUS　via　user　subroutine　and　its　applicability　to　HSS　steels　is　verified.　The　evolution　and　distribution　of　damage　of　HSS　steels　under　various　stress　states　are　studied.　©　2023