<p>Solitary waves are a kind of long-wavelength, high-energy gravity waves that are caused by submarine movements and similar events. Their impact on offshore structures is a typical strongly nonlinear hydrodynamic process that is critical in coastal bridge design. In this study, we develop a Cartesian grid-based numerical framework to simulate solitary wave-bridge interactions. The model is validated against two benchmark cases: solitary wave over a fixed surface-piercing cylinder and solitary wave impacting a box-girder bridge. The numerical results are compared with published experimental data to demonstrate the model’s reliability. Subsequently, the model is applied to simulate the interaction between solitary waves and a box-girder bridge. A series of simulations are systematically conducted with varying wave heights and wave incidence angles. Two wave heights and six wave incidence angles are considered, resulting in a total of twelve cases. The influences of wave height and wave incidence angle on wave run-up and wave impact pressure at typical locations are analyzed in detail. Special attention is paid to the effects of wave incidence angle on the occurrence of wave slamming. The results of this research provide theoretical insights and numerical support for the safety assessment and wave-resilient design of offshore box-girder bridges.</p>