The traversing of elastic waves through fissures is very complex, and there is not an appropriate theory to describe this problem. Based on previous workers' experience, the authors studied dispersive characteristics of Rayleigh waves by using liquid as a substitute for the fissure. Simulation results show that, when there exists a fissure in the foundation, the first mode curve has a cut-off frequency or assumes an interceptive phenomenon. Consequently, the dispersion curves obtained in the investigation consist of multimode guided waves, and there are leaky mode waves at times. The zigzag dispersion curves will occur because of jumping among modes.