Variants of development of the previously obtained results aimed at increasing reliability of description of the subsequent yield surface (SYS) evolution of polycrystalline materials with the help of phenomenological models of the theory of rheonomous plasticity are suggested and briefly substantiated. The results of successful computer simulation of wellknown experiments containing discrepant data on SYS are presented. The introduced phenomenological model permitted to explain the known effect of the influence of the type of unloading on an experimental SYS.