The nonlinear behavior of austenitic stainless steel (ASS) is significantly affected by the temperature and strain during plastic deformation. However, the conventional constitutive model is often inadequate to accurately describe its mechanical properties, particularly at cryogenic temperatures. Therefore, the development of a constitutive model for ASS at cryogenic temperatures is of paramount importance in order to fully understanding the performance of liquefied natural gas (LNG) membrane tank structures under such conditions. In this study, we have derived a modified constitutive model using 304L stainless steel that incorporates a phase transition model through theoretical derivations. First, the stress and strain data for 304L stainless steel within the range of 108–293 K have obtained from quasi-static tensile experiments. Subsequently, the XRD test results are utilized to calculate the volume fraction of martensite across various temperatures and strains. Next, a modified constitutive model is proposed by combining the Olson–Cohen phase transition model and the Swift constitutive model. Finally, the accuracy of the modified Swift constitutive model is verified through experimental data. The results demonstrate that the modified Swift constitutive model is precise for characterizing the properties of 304L stainless steel across a wide range of temperatures. Furthermore, multiple case studies have proven the feasibility of using the modified Swift constitutive model to predict the properties of various austenitic materials. By incorporating the Olson-Cohen phase transition model, the modified Swift constitutive model showcases its wide applicability and potential in designing and assessing the safety of ASS structures.