The effect of a resilient layer isolating a finite cylindrical shell from a high-impedance acoustic medium, e.g., water, on the predominantly radial modes of the shell is explored. While the submerged, bare shell displays resonances whose natural frequencies are reduced below their in vacuo values by the kinetic energy of the entrained fluid vibrating with the same amplitude as the structure, the coated shell displays two families of radial modes: (1) predominantly structural modes whose natural frequencies are raised above those of the shell in vacuo by the coating stiffness, the coating/fluid interface remaining nearly stationary; (2) low-frequency modes embodying the compliant layer's spring stiffness and the combined modal masses of entrained fluid and of the shell; for these modes, coating/fluid interface amplitudes are markedly enhanced above those of the coated shell and even those of the bare, submerged shell.