Abstract:The inversion of pre-stack seismic data needs to take some forward algorithms as a basis.Starting from elastic dynamic equations,the paper adopted slowness method to compute the prestack seismic records in layered medium.The slowness method can provide the complete solution for seismic wavefield like reflectivity method,including the information of primary reflection,multiple and converted wave resulted from propagation of seismic wave in beds and intermediate results can be easily interpreted.The concrete steps of realization is as follows:①the constitutive equations and elastic dynamic equations are transformed into frequency-slowness domain by Fourier transform and Hankel transform;②the recursive formulas of reflectivity and transmissivity matrixes are resulted in frequency-slowness domain;③the seismic data gathers can be resulted from integral transformation for frequency and slowness separately.The stability problem on solution in computing slowness is also discussed in the paper.