The structural continuity of integral bridges has resulted in a long-term, cyclic interaction with the approach backfills leading to two crucial geotechnical consequences, passive lateral stress accumulation, and progressive soil deformation. To investigate these phenomena, numerical methods have been commonly used. However, it is apparent that a majority of utilized techniques are unable to capture the critical facets involved with cyclic loading conditions. Hence, this study presents a comparison of the performance of the widely utilized Mohr–Coulomb (MC) model to that of the bounding surface model proposed by Dafalias and Manzari in 2004 (DM04). Evaluations are made against settlement and lateral pressure data from a scaled physical model of an integral abutment. Results indicate that the MC model is an inappropriate choice, being unable to capture the accumulation of stresses and plastic strains. The DM04 model can reasonably simulate the stress ratcheting response. The propagation of the settlement trough is adequately predicted, particularly at latter cycles. However, the variation in the rate of change of maximum settlements with the progression of cycles is anomalous from typical behavior.