We present an analytic and numerical study of Whispering Gallery‐type surface‐ wave modes on solid elastic cylinders imbedded in a fluid. The complex wave numbers of these waves are obtained for the case of high frequencies (ka≳15), including both their attenuation and dispersion curves for the phase velocities. It is shown that there are two different groups of Whispering Gallery modes whose wave numbers in the limit of infinite frequency or infinite cylinder radius approach the corresponding wave numbers of compressional and shear bulk waves in the cylinder material.Subject Classification: [43]40.20; [43]30.50; [43]40.55; [43]20.15; [43]35.54.