We　presented　an　elastic-plastic　endochronic　constitutive　model　of　0Crl7Ni4Cu4Nb　stainless　steel　based　on　the　plastic　endochronic　theory　(which　does　not　need　the　yield　surface)　and　experimental　stress-strain　curves.　The　key　feature　of　the　model　is　that　it　can　precisely　describe　the　relation　of　stress　and　strain　under　various　loading　histories,　including　uniaxial　tension,　cyclic　loading-unloading,　cyclic　asymmetric-stress　axial　tension　and　compression,　and　cyclic　asymmetric-stress　axial　tension　and　compression.　The　effects　of　both　mean　stress　and　amplitude　of　stress　on　hysteresis　loop　based　on　the　elastic-plastic　endochronic　constitutive　model　were　investigated.　Compared　with　the　experimental　and　calculated　results,　it　is　demonstrated　that　there　was　a　good　agreement　between　the　model　and　the　experiments.　Therefore,　the　elastic-plastic　endochronic　constitutive　model　provides　a　method　for　the　accurate　prediction　of　mechanical　behaviors　of　0Crl7Ni4Cu4Nb　stainless　steel　subjected　to　various　loadings.　Copyright　©　2016　Jinquan　Guo　et　al.