The steady-state axisymmetric radial vibrations of a circular cylindrical shell of infinite length subject to an annular load moving along its axis following the law x//1 equals r cos omega t are analyzed. In the first approximation this scheme can serve as the theoretical model for studying the vibrations caused by piston ring motion in a cylinder. The model makes it possible to determine the resonant load velocities and also the displacements and stresses in the shell.