A class of one-dimensional models for the yielding behavior of materials and structures is presented. This class of models leads to stress-strain relations which exhibit a Bauschinger effect of the Massing type, and both the steady-state and nonsteady-state cyclic behavior are completely specified if the initial monotonic loading behavior is known. The concepts of the one-dimensional class of models are extended to three-dimensions and lead to a subsequent generalization of the customary concepts of the incremental theory of plasticity.