In this paper, the first-order ordinary differential constitutive equations of endochronic theory are incorporated into finite element formalism. A theoretical investigation is performed on the ratchetting effect of a stepped beam subjected to steady tension and cyclic bending. Experimental data of lead alloy found in literature are used for comparison. Those data reveal that the endochronic prediction yields more adequate results than those predictions using the plasticity models with isotropic hardening or kinematic hardening, as employed by Hardy, et al. (1985).