Recent interest in applications like the measurement of compressive surface residual stresses due to shot peening using Rayleigh type surface acoustic waves have brought into the spot light the adverse effects surface roughness might have on such measurements. Surface roughness produces significant dispersion of the Rayleigh wave used in the measurements. Therefore an accurate understanding of the effect of surface roughness on the dispersion of Rayleigh waves is of crucial importance for this application and others in which surface roughness is a natural by‐product of the manufacturing processes used to produce the part. In this paper, the dispersion of Rayleigh surface wave on a 2D‐randomly‐rough surface is studied numerically using Wave2000Pro, finite difference wave propagation simulation software. First the dispersion of the wave due to the discretization of the model is investigated to establish the accuracy of the model. Wave 2000Pro is then used to analyze the dispersion of Rayleigh wave propagating on the rough surface. The results of the numerical analysis are then compared to the calculations of Kosachev and Shchegrov. © 2004 American Institute of Physics