Equipment and pipes are the main components of a nuclear power plant (NPP) that ensure transfer of heat energy into electric one. The pipes with nominal diameter from DN10 to DN1200 are the main types of pipes that also include different fragments such as bends, cones, tees, branches, etc. Common length of all NPP pipes is hundreds of kilometers. All these components can be combined by one common feature: they are shell structures that found wide application in daily activities. The use of such components in the design and manufacture of equipment and pipelines of NPP power units requires appropriate practical and theoretical studies. The use of filler made of light materials allows for a small increase in the weight of the structure to significantly increase its bending stiffness and improve its thermal insulation properties. The oscillations of three-layer cylindrical pipes are considered in this paper. The equations of motion of a three-layer cylindrical shell with lightweight filler reinforced by stiffening ribs with non-stationary loading have been provided through these efforts. The model of Timoshenko’s theory of shells and rods have been used in this study under analysis of components with flexible structures. Numerical results of oscillations of the three-layer elastic structure were obtained using the finite element method. The impact of the physical and mechanical parameters of the shell layers is investigated on its stress strain state under an axisymmetric internal impulse loading.