Mountain tunnels across adverse geological structures (e.g., faults, fracture zones, joints, interface between hard and soft rock, etc.) are more vulnerable to damage than in competent rock under earthquake loading. However, the understanding of seismic response of deep-buried tunnels crossing double or multiple faults is still unknown. In this regard, a two-dimensional DEM model was established to reveal the seismic response of a deep-buried tunnel in poor surrounding rock containing double parallel faults. The effects of fault dip angles and rock mass quality on the mechanical behavior of tunnel structures were analyzed. Numerical results show that double parallel faults with a large dip angle (in the range from 45°–75°) may be more unfavorable for the safety and stability of the tunnel. The vertical relative displacement of the lining is approximately equal to or even larger than the horizontal relative displacement. As the rock mass quality varies, the lining structure deforms in rigid deformation, compressive shear deformation, and convergence deformation modes for the Down-Cross Fault and Up-Cross Fault scenarios, while in only shear failure mode for the Cross-Cross Fault scenario.