Three-dimensional finite element method is utilized to analyze the plasticity-induced crack closure (PICC) phenomenon in a cracked plate under variable amplitude loading conditions: the effect of a single spike tensile overload, and also the case of a single compressive overload (underload). To accurately capture the PICC process the choice of material model employed is of significant importance, therefore this paper considers a relatively new model, the Ellyin-Xia model, and the more widely employed kinematic hardening model. The study shows significant difference in the results obtained while employing the two models.