It is shown experimentally and theoretically that waves propagate around circular cylindrical shells with a phase velocity that is less than the phase velocity of sound in water. These waves are called Scholte–Stoneley waves. First this paper presents results on air‐filled aluminum pipes of different ratios of the internal radiusbto the external radiusa. The frequency resonances and the ordersnof the resonances increase with theb/aratio. The frequency range of the observed resonances is fixed for a given pipe. This is related to the evolution of the resonance width with frequency. The frequency resonances and their width are calculated with the use of the resonance scattering theory. The so obtained results agree quite well with the experimental ones. The Scholte–Stoneley wave, which propagates around the shell, is compared to the antisymmetric Lamb wave, which appears on a thin plate when the plate is imbedded in water. Second, the influence of the internal fluid on the Scholte–Stoneley resonances is studied. Three different liquids are used: water, chloroform, and glycerol. The experimental results agree once more with the theoretical ones.