The 'finite element' technique is used to investigate numerically the guiding of elastic surface waves by ridges with a view to application in microwave electronics and in seismology. The technique is applied first to other problems with a cylindrical geometry such as the propagation of waves along bars and plates where existing theoretical and experimental results are available for comparison. Finally ridged structures are considered. Dispersion curves and displacement functions are obtained for the lowest mode which is the only one which may, under suitable circumstances, propagate unattenuated. Our results indicate that only the lowest antisymmetric mode is properly trapped by the ridge and that this occurs in a certain frequency range.