Many engineering materials appear an independent from the kind of loading elastoplastic material behavior. With respect to the sign convention we get, for instance, the same stress-strain diagrams for tension and compression. For materials which contain voids, pores, etc., different elastoplastic stress-strain curves can be obtained in tension and compression tests. In addition to these experimental observations, such materials often show inelastic volumetric deformations. Grey cast iron is a typical example of this kind of material. Constitutive equations for this special elastoplastic behavior are derived as a particular case of generalized constitutive equations for isotropic materials based on a potential. The yield condition is established on the second invariant of the stress deviator and, additionally, on the first invariant of the stress tensor and on a hardening parameter. The plastic potential depends on the same arguments, but a nonassociated flow rule is assumed. For the hardening function, a modification of the plastic work hardening model is used. All parameters of the model are identified by tests. The verification is realized by different independent tests.