Abstract: Clarifying the dynamic response characteristics of soil-rock strata under transient waves is of great significance for accurately evaluating and controlling the dangerous effects of dynamic effects such as blasting or earthquake. Aiming at the typical soil-rock stratum structure, the standard linear solid is introduced to describe the soil constitutive, and the physical analysis model of soil-rock stratum under transient wave action is constructed. Based on the characteristic line method and the displacement continuity method, the explicit mathematical description of transient wave propagation in soil-rock stratum is established. Finally, through parameter analysis, the influence of dimensionless thickness, relaxation time and equivalent dynamic modulus of soil on the propagation characteristics and site amplification effect of transient wave in soil-rock stratum is systematically discussed. The results show that: (1) when considering the viscoelasticity of soil, the amplification effect of surface site is small; (2) With the increase of dimensionless thickness, the particle velocity amplification effect of soil-rock interface decreases first and then stabilizes, the peak value of stress wave increases first and then decreases, and the surface velocity amplification effect increases first and then decreases. (3) With the increase of relaxation time, the amplification effect of interface vibration velocity is basically unchanged, the surface amplification effect increases first and then stabilizes, and the peak value of stress wave increases gradually. (4) With the increase of equivalent modulus, the amplification effect of surface and interface vibration velocity is almost unchanged, and the peak value of stress wave decreases gradually.