The well-known Olson–Cohen model is modified by incorporating the effect of stress state on the transformation kinetics in metastable austenitic stainless steels. By assuming isothermal condition, the relationships between the parameters of Olson–Cohen model, stress triaxiality and absolute value of Lode angle parameter have been established. The proposed model predicts that the saturation level and slope of transformation curve increase with increasing the stress triaxiality in addition to the absolute value of Lode angle parameter. Uniaxial and plane strain tension tests have been conducted on the two types of austenitic stainless steels AISI 304 and AISI 201 to evaluate the validity of the model. The results show that the predicted transformation curves are in good agreement with the experimental data.