The dispersion behavior of circumferential creeping waves around a fluid-filled cylindrical cavity in an infinite elastic medium is analyzed by computational methods. Phase and group velocity as well as attenuation curves are constructed by numerically solving the dispersion equation. A comparison of the corresponding modes for elastic and rigid hosts is presented. The modes in both cases exhibit essentially the same series of cutoff frequencies corresponding to radial resonances at which the phase velocity of the associated modes becomes infinite and the group velocity assumes a limiting value ofπcf/2,wherecfis the compressional wave velocity in the fluid. Attenuation of the circumferential creeping modes in a cylindrical cavity is caused solely by losing energy to the surrounding elastic bulk. Therefore, for all modes, the attenuation diminishes at high frequencies as leakage into the surrounding solid becomes negligible. This is in sharp contrast with the case of leaky Rayleigh wave propagation along the plane surface of a solid–fluid interface where attenuation is caused solely by radiation of energy into the fluid, which causes the frequency to have an opposite effect on the degree of leakage in these situations.