In earthquake-prone areas, mountain tunnels often suffer from seismic damage when traversing active fault zones. To capture the seismic behavior of mountain tunnel under the action of active faults motion, the rate and state friction (RSF) relation is introduced to define the stick–slip dynamic behavior of a fault. The RSF relation is implemented in the finite element methods (FEMs). Numerical simulations of triaxial patch tests indicate that the RSF method can effectively capture the stick–slip dynamics. To reproduce the seismic damage to Daliang tunnel caused by slip of the Lenglongling fault, a three-dimensional (3D) numerical model including tunnel structure and plates of the fault is established. Seismic waves triggered by fault slip are then reproduced using the model. The simulation results show that the waves are dissipated while travelling and that their amplitudes decrease with depth. The failure of the tunnel lining is captured, and its seismic responses, including the displacement and strain of the structure, are extracted for various fault strike angles. The simulations are consistent with the observations, and it indicates that the movement of the simulated tunnel structure adjacent to the fault surface is significantly greater than those in the foot wall and in the middle of the fault. This study has the potential to provide a more direct means of understanding the seismic action of infrastructure induced by earthquakes. Seismic waves are no longer needed as input to the numerical simulation and instead, the earthquakes are generated by directly modeling the stick–slip motion of the fault.