Rayleigh waves are surface waves which are dispersive in layered media. In order to study Rayleigh wave dispersion, there are several methods. Among these methods the application of matrix methods for elastic layered media is preferred to other methods. In the matrix method for a layered medium, boundary conditions for different interfaces are satisfied to obtain a relation for calculating Rayleigh wave dispersion which should be resolved by numerical methods. A program for the computing of Rayleigh waves dispersion was developed. The resulted dispersion curves from this program were compared to similar methods which showed good agreement. According to the resulted graphs, wherever the earth structure is complex the dispersion curves also will be complex and different models will be moved oscillatory. Phase and group velocity curves tend to lower values when there are a surface sedimentary layer in the earth model. Thus, synthesis of these curves leads to clarification of different seismic phases, history of waves propagation from source to receiver and consequently imaging of earth structure