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. oft-com:office:office" />