In a previous paper [6] we considered the problem of finding the stresses and displacements in a body made up by an elastic-perfectly plastic material under a given time-dependent load. Following Duvaut-Lions [3] this problem was formulated as a variational inequality, and we proved existence of a (strong) solution of the variational inequality. In this note we shall carry out the same program in a more general case of a hardening elastic-plastic material. The properties defining an elastic-plastic material in mechanics are usually taken to be (i) the yield condition, (ii) the flow rule and (iii) the hardening rule. One of the most well-known models in mechanics for plasticity is based on the von Mises yield condition, the Prandtl-Reuss flow rule and isotropic or kinematic hardening. The main assumption in this note concerning the elastic-plastic material is that the yield condition can be written