Abstract: Under strong earthquakes, the prescribed boundary displacement input from strike-slip faults induces highly nonlinear responses and complex localized failure modes in cross-fault bridges. Taking a three-span simply supported girder bridge equipped with expansion joints as the research object, a three-dimensional (3D) nonlinear finite element model of the cross-fault structure was developed to quantitatively elucidate the governing laws of peak fault rupture displacement, permanent displacement, and crossing angle θ on the dynamic evolution characteristics of critical components. The results demonstrate that the peak displacement primarily governs the transient excitation of the bridge; its increase triggers a drastic surge in displacement responses and severe pounding at girder ends, causing the plastic damage of piers to propagate into deeper sections. Conversely, the permanent displacement dominates the steady-state residual response of the structure, and its escalation leads to accumulated damage and the shear coordination failure of expansion joints. Furthermore, the crossing angle serves as the critical physical variable controlling the anisotropic structural response; variations in this angle significantly modify the spatial distribution of fault displacement components, thereby fundamentally altering the internal force distribution of piers, the deformation modes of bearings, and the dislocation patterns at girder ends. The findings of this study provide a solid theoretical basis for the seismic mitigation design and performance evaluation of cross-fault simply supported girder bridges.