Abstract In the present study, a viscoplastic constitutive model is developed based on the results of uniaxial tensile tests on austenitic stainless steels AISI 316L, 321, and 347. Because austenitic stainless steel exhibits nonlinear plastic behavior at low temperatures, investigating the mechanical characteristics and the constitutive equation is necessary. First, mechanical characteristics such as the hardening effect and the strain-rate effect are analyzed by introducing the strain–hardening rate. Second, a constitutive equation is developed based on the Bodner–Partom viscoplastic model for describing the nonlinear hardening behavior. The Bodner–Chan damage model is then coupled with the viscoplastic model for describing the material degradation, and its material parameter identification method is introduced. Finally, to verify the effectiveness of the proposed equation, a user-defined material subroutine (UMAT) interface, which is offered by the finite element software ABAQUS, is developed. The numerical analysis results are compared with tensile testing results to conduct a feasibility study.