The stress at the structural plane of bedding rock slope will change under dynamic load, which may lead to sliding failure risk of the slope. Based on the time-domain recursive method (TDRM), the propagation process of stress waves in viscoelastic rock slope with a nonlinear bedding plane is analyzed, and the propagation equation of multiple reflected waves between the plane and the slope surface is obtained. According to the superposition principle and the relation between the particle vibration velocity caused by stress waves and stress, the expressions of normal and tangential stress of any particle at the structural plane are obtained. Furthermore, in light of the gravitational impact on the rock mass, we formulate the slip criterion equation for the structural plane. The results indicate that the stress field at the structural plane is influenced by several factors, including the slope angle, horizontal positioning of monitoring points, vertical distance to the slope foot, and the initial stiffness of the structural plane. The influence of multiple reflected waves on stress field obviously increases the possibility of rock mass sliding on structural plane. This paper theoretically elucidates the slippage mechanism of a rock slope featuring a bedding structural plane subjected to the effects of stress wave. The research findings furnish a theoretical foundation for comprehending the dynamic response of rock slopes, conducting dynamic stability analyses, and ensuring the safety measures for rock mass engineering projects.