Dynamic transient processes are studied and the results of evaluating the influence of an elastic medium on the behavior of a three-layer cylindrical shell structure of elliptical cross-section under non-stationary impulse loading are given. The used model of the theory of shells and rods by S. P. Tymoshenko, taking into account independent static and kinematic hypotheses for each layer of the structure. Numerical calculations of normal deflections and normal stresses of the load-bearing layers of the structure, which determine its stress-strain state (SSS), have been performed. Variants of the structure without a polymer aggregate and with a discrete-symmetric rib-reinforced aggregate are considered. A comparative analysis of the deflections and stresses of the load-bearing layers of the structure in the absence of light aggregate and in its presence is given.Numerical results regarding the dynamics of the three-layer structure were obtained using the finite element method.