The equations of non-axisymmetric vibrations of three-layer elliptical cylindrical shells with reinforcement rings under non-stationary loading are derived. The elements of this elastic structure are described using the refined Timoshenko-type model of shells and rods. The numerical method of solving the dynamic equations is based on the integro-interpolation method of constructing the finite-difference schemes for equations with discontinuous coefficients. The problem of the dynamic behavior of a three-layer elliptical cylindrical shell with discrete ribs under distributed non-stationary loading is solved. The numerical results are given in the form of plots and analyzed.