By using the incremental form of the endochronic theory of plasticity, a model of material function is proposed in this paper to investigate plastic behavior. By comparing the stress-strain hysteresis loop, the theory is shown to agree well with the experimental results, especially in the evolution of peak stress values of SAE 4340 steel loaded by cyclic loading with various amplitudes. Depending on the choice of material parameters, the present model can substantially result in six categories of material function, each of which can behave differently with respect to an identical deformation history. In addition, the present model of material function is shown to be capable of describing the behavior of erasure of memory of materials, as experimentally observed by Lamba and Sidebottom (1978).