Abstract: The problem of random wave traveling along stratified media is important for earthquake engineering. The rock strata are considered as multi-layered and located above the base-rock, whose material property is assumed to be much stiffer than the above strata; and the power spectrum density of the random excitation is given at the base-rock. The rock strata can be arbitrarily anisotropic for each layer. The governing differential equations are derived in frequency and wave-number domain and only a set of ordinary differential equations should be solved. The precise integration algorithm is applied to solve the ordinary differential equations. Thereafter, the recently developed pseudo-excitation method for structural random vibration is transplanted to the solution of the layered rock responses. Numerical results are given and compared with some classical results. And that show the reasonability of the presented method.

Key words: earthgquake wave, large-span bridge, random vibration, spatial effect