The two-dimensional finite element method is employed to simulate Rayleigh waves in this study. Various dislocation sources located at various depths are considered. Through the analysis of amplitude variations, the relationships between the excitations of the Rayleigh waves and the faultings are gradually understood. In order to determine the effects due to the damping factor involved in the calculations from the attenuation curves, a simple technique is proposed and applied in this paper. The results show that the amplitude is suppressed to a lower extent with lower frequency signals. In general, Rayleigh-wave excitation from any type of faulting decreases with source depth. The steeper finite faultings at the shallower depth generate stronger Rayleigh waves. For 45 degree dip-dip sources, it is also easier to generate stronger Rayleigh waves for point sources than for finite ones.