Previous investigation concerning the scattering of elastic waves from solid spherical inclusions have furnished expressions for the scattering cross sections which, upon numerical evaluation, exhibited resonancelike features as a function of frequency. In the present work, we study these resonances in a fashion suggested by the resonance theory of acoustic scattering due to Flax, Dragonette, and Überall [J. Acoust. Soc. Am. 63, 723 (1978)]. The resonances of the solid inclusions, exemplified by iron or lucite spheres imbedded in an aluminum matrix, are found numerically in the individual normal‐mode scattering amplitudes, and are interpreted in terms of phase‐matched circumferential waves. Dispersion curves for the phase velocities of the latter are obtained, exhibiting two families of waves of different type. Finally, the connection of these waves with the Stonely waves on the boundary between two flat half‐spaces is noted in high‐frequency limit.