The three-layer cylindrical shells with elliptic cross-section with regard for a cross-ribbed discrete filler are studied. According to the Timoshenko hypothesis for shells and ribs, the corresponding wave equation is de duced. In the solution of the specific boundary-value problems, an explicit finite-difference scheme of integration of the equations is used. As a numerical example, a solution of the problem of forced oscillations of a not axisymmetric heterogeneous shell structure under the action of a distributed unsteady load is given.