Abstract: Lagrange discontinuous deformation analysis (LDDA) and the earthquake free field input model for the slope analyses with the spring-viscous boundaries are simply introduced, in which LDDA is used to model faults, joint cracks, and fracture structure planes. The Bai He Tan left rock slope is calculated and analyzed by the model. The coefficient of reduced strength and earthquake-overloading factors are introduced, thusly the relationship among these coefficients and dynamic displacement, as well as joint opening is established. The results show that the strength-reserve-safety factor of reinforced Bai He Tan left rock slope under a design earthquake is about 1.18, earthquake-overloading safety factor is about 1.25. The present analysis method, different from that using rigid limit equilibrium, is an optional power tool for slope dynamic stability analyses.