Of studies on the vibrations of structures in the form of cylindrical shells under kinematic excitation of any point of the surface, have been relatively few, although the practice of engineering and construction such problems arise quite often. With this kind of problem is faced, for example, when transporting goods by road, rail and sea transport, as well as the analysis of the resistance of structures during earthquakes. This article discusses the behavior of orthotropic shell, reinforced by circular ribs and isotropic cylinder and suspended on springs, given the harmonic movement of her butt. Internal friction in materials envelope, the edges of the cylinder and taken into account by the complex elastic modulus according to the hypothesis Sorokin. The solution obtained differential equations of motion envelope, the edges of the cylinder and is sought by presenting features double trigonometric series in the axial and circumferential coordinates. As a result, the problem is reduced to a system of algebraic equations for the amplitude values of the normal movement of the ribs in the places of installation of springs. In the numerical example illustrates the effect of changes in individual parameters on the dynamics of the whole system.