The acoustic scattering from infinite cylinders or spheres has shown the great influence of surface wave propagation. Two types of surface waves are distinguished: the Rayleigh or Whispering Gallery waves and the Scholte–Stoneley waves. In this study, experimental results obtained on the finite cylindrical shells bounded by two hemispherical endcaps are presented. These objects are made of stainless steel and filled with air. Their radius is 27 mm and their radius ratio b/a is 0.97 (b is the inner radius and a the outer radius). The direction of insonification is parallel to the main object axis. The reduced frequency range k1a of the study varies from 10 to 40. These experimental results are explained by writing the stationary condition on the large circumference of objects, in the meridian plane. This condition depends on the phase velocity in the length of the cylindrical shell and in the spherical shell. These two velocities are computed separately in relation to the frequency and used to apply the stationary condition. The obtained results are in good agreement with the experimental study.