Behavior of compound shell structures under local loads has not been adequately investigated. We study forced vibrations of a layered ring supported by two orthotropic layered cylindrical shells and an orthotropic semi-sphere. A harmonic load uniformly distributed over a local zone of the ring is applied to the structure. The inner surface of one of cylindrical shells attached to an elastic hollow cylinder. According to the hypothesis by E.S. Sorokin, we use complex modules to account for visco-elastic properties of the system under consideration. We represent displacement functions in terms of a trigonometric series with respect to an angular co-ordinate. To solve ordinary differential equations obtained, we employ the method of boundary parameters.