In　order　to　study　the　constitutive　relation　of　stainless　steel　under　cyclic　loading,　austenitic　stainless　steel　S30408　and　duplex　stainless　steel　S220503　coupons　were　tested　under　monotonic　and　large-strain　ultra-low　cyclic　loading.　Three　types　of　constitutive　models　were　used　to　fit　the　stress-strain　relationship　under　monotonic　loading,　and　pertinent　constitutive　relation　parameters　were　obtained.　The　cyclic　skeleton　curves　were　fitted　by　the　Ramberg-Osgood　model,　and　the　parameters　of　the　cyclic　hardening　were　calculated.　Furthermore,　the　parameters　of　the　cyclic　constitutive　model　were　calibrated　and　the　test　curves　were　simulated　by　ABAQUS　finite　element　analysis　software.　The　results　show　that　the　G-R-O　constitutive　model　can　fit　the　constitutive　relation　better　under　monotonic　loading.　Under　cyclic　loading,　with　the　increase　of　cyclic　loops　and　change　in　strain　amplitudes,　stainless　steel　exhibits　a　cyclic　hardening　behavior.　The　Ramberg-Osgood　model　fit　the　skeleton　curve　well　and　the　simulated　curves　agree　fairly　well　with　the　test　curves.　Therefore,　the　hardening　parameters　and　cyclic　constitutive　parameters　which　calibrated　by　the　test　data　can　be　applied　to　the　structural　seismic　analysis,　and　improve　the　accuracy　of　analysis　for　the　stainless　steel　structure　under　earthquake.　©　2019,　Engineering　Mechanics　Press.　All　right　reserved.