Abstract Classical models based on the thermodynamics of irreversible process with internal variables dedicated to the inelastic analysis of metallic structures are modified and then used for modeling the mechanical behavior of polymers. The major difference comes from the expression of the yield criterion. Indeed, a generalized yield criterion, based on the parabolic Drucker and Prager criterion, is proposed including the first invariant of the stress tensor as well as the second invariant and the third invariant of the deviatoric part of the stress tensor. Close agreement between experimental data and yielding predictions is obtained for various polymers loaded under different states of stress. It has been established that the temperature T, the strain rate s ˙ , the critical molecular mass M c and the degree of crystallinity X c do not affect the parameter m of the proposed yield function. Furthermore, viscoplastic constitutive equations are developed in the framework of the general principles of thermodynamics with internal variables for generalized materials considering only the kinematic hardening rule. Experimental data obtained under different loading conditions are well reproduced by the proposed model. An accurate identification of the model parameters and the introduction of the isotropic hardening variable into the yield function and the drag stress will improve the predictions of the overall mechanical behavior of polymers especially the unloading path.