Rayleigh waves propagating in an elastic surface are commonly used for the near surface flaw detection and material characterization. However, unlike the bulk wave case, there are seldom three-dimensional models to be provided for the Rayleigh waves. In the past decade, multi-Gaussian beam models have been gradually developed and perfectly applied to solve many complicated propagation problems of bulk waves. However, up to date they have not been extended to the simulation of the Rayleigh waves. By combining the Rayleigh wave Green function and the multi-Gaussian beam model, a three-dimensional Rayleigh wave model is presented to calculate the beam fields radiated from a rectangular transducer mounted on the Lucite wedge. Furthermore, some simulation results of the provided method are compared to those of a more exacted point source model. It is shown that the multi-Gaussian surface wave model has good capability in both computational accuracy and efficiency.