An issue of a stress-strain state of a three-layer cylindrical shell under variable loads has been considered. Assessment results of a three-layer cylindrical shell stress-strain state with regard to the physical and mechanical characteristics of an aggregate polymer filler and its reinforcement intensity by means of the stiffening rings rigidly connected to the shell coating are presented in the article. Calculations have been performed using the software Nastran. Values of displacements and stresses have been calculated by applying the direct transient dynamic process algorithm. The time interval was 0.0000025 sec, and the total number of steps was 200. Choice of the three-dimensional finite element type was conditioned by the need of acquiring more detailed and accurate calculation results. The finite element model included 8000 three-dimensional solid finite elements and 9360 nodes. Impact of the physical and mechanical characteristics’ parameters of integral polymeric filler through the stiffening rings on the shell’s stress-strain state under the axisymmetric inner impulse load has been investigated. Numerous results concerning dynamics of the three-layer structure, which have been obtained by the finite elements method, allow distinguishing the stress-strain state of a three-layered cylinder-type elastic structure at any moment within an analyzed time interval. Optimization of the shell design is recommended. Intensity of the polymeric filler reinforcement impacts considerably the stress-strain state of the shell, as well as its performance characteristics. Increasing the intensity of the shell’s polymeric layer reinforcement decreases considerably the deformation of the shell’s bearing layers. Comparison of the obtained results to the impact of other factors indicates the credibility of the approach used and that the unbiased information was received.