Abstract: The propagator matrix approach Abo-Zena based on the dispersion equation of Rayleigh wave could only be used for studying dispersion characteristics of layered media.For non-layered media,the propagator matrix approach was useless,and the finite-element method and the finite-difference method had to be considered.The authors applied the finite-difference method to simulate full-wave-fields in an infinite half-space filled with homogeneous elastic solid medium.The modeling program was written out in Matlab environment.The propagation characteristics of Rayleigh wave reappeared in snaps.A kind of algorithm to draw and fill the wiggle curves of the seismic synthetic records was also achieved,and more realistic seismograms were obtained.According to the modeling results,there is serious numerical dispersion by using one order finite-difference method,and the numerical dispersion must be suppressed when zigzag dispersion will be studied by finite-difference method in the future.Then,more realistic dispersion curves can be obtained.