Predicting the response of elastomeric seismic isolation bearings when subjected to severe ground motions is challenging due to the highly nonlinear behavior associated with the bearings under a combination of large displacements and axial loads. In particular, the horizontal stiffness of the bearings is a function of both horizontal displacement as well as axial load that varies due to overturning moments. Previous analytical models or formulations to model these bearings were mainly developed to estimate critical loads at the stability limit. Only few of these models are capable of estimating the correct nonlinear behavior of bearings observed at horizontal displacements in excess of the bearing width. In this study, a nonlinear analytical model is presented that is capable of modeling the dynamic response of bearings more accurately at all displacement ranges, especially beyond the stability limit and is verified with experimental data from an earlier experimental study. It was observed in the dynamic experiments that the bearings have a far larger capability to sustain horizontal loads at displacements exceeding their stability limit than predicted by earlier models and more importantly the bearings re-centered after these large displacement excursions. This behavior is captured using the analytical model developed in this study.