Recent experiments on metals have shown that all of the stress invariants should be involved in the constitutive description of the material in plasticity. In this paper, a plasticity model for metals is defined for isotropic materials, which is a function of the first stress invariant in addition to the second and the third invariants of the deviatoric stress tensor. For this purpose, the Drucker–Prager yield criterion is extended by addition of a new term containing the second and the third deviatoric stress invariants. Furthermore for estimating the cyclic behavior, new terms are incorporated into the Chaboche's hardening evolution equation. These modifications are applied by adding new terms that include the effect of pervious plastic history of deformation on the current hardening evaluation equation. Also modified is the isotropic hardening rule with incorporating the effect of the first stress invariant. For calibration and evaluation of this plasticity model, a series of experimental tests are conducted on high strength steel, DIN 1.6959. In addition, finite element simulations are carried out including integration of the constitutive equations using the modified return mapping algorithm. The modeling results are in good agreement with experiments.