A numerical model based on the theory of fluid-structure interaction is developed by finite element method to simulate the laser thermo-elastic generation and propagation of interface waves at the fluid-solid interface. The propagation characteristics of leaky-Rayleigh wave,Scholte wave and lateral wave are analyzed,and the numerical solution of full wave field is obtained. Furthermore,the effect of different fluid media on the waveform of interface waves is discussed. The results show that various modes of fluid-solid interface waveform are excited simultaneously by pulsed line source,with the waveform significantly affected by the material parameters of liquid media. The numerical simulation establishes a quantitative relation between the laser parameters,the material parameters and the corresponding waveform.