Acoustic waves normally incident on an elastic cylindrical shell can cause the excitation of circumferential elastic waves on the shell. These shells may be empty and fluid immersed, or fluid filled in an ambient medium of air, or doubly fluid loaded inside and out. Circumferential waves on such shells have been investigated for the case of aluminum shells, and their phase‐velocity dispersion curves have been obtained for double fluid loading [Bao, Raju, and Uberall, J. Acoust. Soc. Am. 105, 2704 (1999)]. Similar results were obtained for empty or fluid‐filled brass shells [Kumar, Acustica 27, 317 (1972)]. We have extended the work of Kumar to the case of fluid‐filled aluminum shells and steel shells imbedded in air. These cases demonstrate the existence of circumferential waves traveling in the filler fluid, exhibiting a certain simplicity of the dispersion curves of these waves. This is in striking contrast to the results for double (outside and inside) loading by two fluids of comparable density, where...