Based on the propagation theory of elastic waves in frozen poroelastic media and elastic media, a theoretical model of saturated frozen soil and elastic solid bedrock is established. The saturated frozen soil is lying on an elastic solid bedrock and is modeled as a porous material containing a three-phase medium that contains two solids (soil skeleton and ice particles) and a compressible viscous fluid. Based on the Helmholtz vector decomposition and the boundary conditions on the interface, the theoretical expressions of the amplitude ratio and displacement of the plane S1 wave incident from the saturated frozen soil to the elastic solid bedrock interface are obtained. The effects of incidence angle, frequency, cementation parameters, saturation, and contact parameters on amplitude ratio and displacement were investigated. The results indicate that only S wave and horizontal displacement exist when the incident angle = 0°. As cementation parameters, saturation, porosity, and contact parameters increase, the critical angle appears earlier. Each wave has different degrees of pulses when reaching the critical angle, among which the transmitted P wave and the reflected S2 wave are the most significant. At higher saturation, it is observed that the amplitude ratio of the reflected S2 wave decreases significantly. The horizontal and vertical displacements increase significantly with increasing frequency.