The notion of Plastic Internal Variables (PIV) is used in reformulating, in a general form, the equations of rate-independent plasticity. The stress, temperature, and the PIV are the state variables for the present development. Loading-unloading is defined in terms of the usual loading function of classical plasticity. The concept of discrete memory parameters entering the constitutive equations for the PIV is introduced, in order to describe realistically the material behavior under cyclic loading. Within the framework of the general development, a simple model is constructed. By generalizing uniaxial experimental observations the concept of the “bounding surface” in stress space is introduced, defined in terms of appropriate PIV. This surface always encloses the yield surface, and their proximity in the course of their coupled translation and deformation in stress space during plastic loading determines an appropriate quantity function of the state variables and a corresponding discrete memory parameter on which the value of the plastic modulus depends. The model is compared with experimental results in a uniaxial case.