Previous　studies　have　established　a　variety　of　cumulative　damage　models　(CDMs)　for　either　structural　materials　or　members　to　perform　an　exquisite　evaluation　on　plastic-induced　deterioration　of　structural　engineering　under　severe　seismic　actions.　Nevertheless,　the　existing　CDMs　consider　different　influencing　factors　and　hence　tend　to　produce　significantly　different　simulation　performance.　On　the　other　hand,　the　influencing　variables　of　CDMs　are　likely　affected　by　the　description　on　the　cyclic　stress-strain　relation.　Thus,　the　quantification　of　seismic　damage　is　affected　by　the　selection　of　both　CDM　and　constitutive　model.　Existing　relative　studies　mainly　focus　on　the　development　and　refinement　of　theoretical　models.　However,　the　understanding　on　simulation　performance　difference　induced　by　the　selection　of　models　is　still　limited.　This　paper　is　aiming　to　clarify　the　influence　of　different　constitutive　models　and　CDMs　on　the　cumulative　damage　behaviors　simulated.　Firstly,　three　types　of　cyclic　constitutive　models　and　nine　CDMs　are　reviewed　and　their　material　parameters　are　summarized.　The　CDMs　selected　include　the　deformation-type　models,　the　energy-type　models　and　the　combined-type　models.　Based　upon　different　CDMs,　the　low-cycle　fatigue　(LCF)　curves　of　mild　structural　steel　are　generated　and　compared　to　the　corresponding　Coffin-Manson　relations.　Subsequently,　the　damage　evolutionary　curves　of　different　CDMs　are　simulated　based　upon　several　representative　cyclic　loading　protocols.　The　influence　of　constitutive　models　and　CDMs　on　the　LCF　curves　and　damage　evolutionary　curves　are　thoroughly　studied.　Besides,　the　sensitivity　of　CDMs　on　strain　ratios　and　the　influence　of　cyclic　loading　protocols　on　damage　evolutionary　curves　are　simultaneously　clarified.　The　research　findings　can　lay　a　solid　foundation　for　the　selection　and　combination　of　the　relative　analytical　models　with　regards　to　different　circumstances.　©　2023