Abstract The use of Rayleigh waves enables the solution of several important inspection problems. Propagation of surface waves along straight boundaries has been properly studied but investigations about their propagation on cylindrical surfaces are not sufficient, despite they can be still of interest for NDE applications. It has been proved experimentally that a surface wave pulse suffers a phase shift during its propagation along a cylindrical surface. A numerical approach has been developed to efficiently study these effects for different materials, curvatures and frequencies. This study can help the scientific community to better understand the phenomenon, quite complex and not yet fully explored.