The scientific paper presents a technique for calculating a thick-walled axially symmetrical construction consisting of a steel rod (reinforcing component) and an external thick-walled shell made of carbon fiber. The construction is loaded with linear load distributed along its length, associated with the operating external pressure, and inertial forces. The technique is based on a one-dimensional model of a composite rod of variable cross-section, roughly taking into account transverse deformations, which is necessary when analyzing a thickwalled construction operating under pressure. In the proposed approach, the geometry of the product is divided into sections and approximated by fragments in the form of truncated cones and, in the particular case, in the form of cylinders. As a result of calculations, the distribution of normal tensile/compression stresses in the shell and in the reinforcing rod, as well as tangential stresses at the boundary of their contact, are determined. As a result of test calculations, a fairly good consistency of the considered one-dimensional model with refined finiteelement modeling is shown. It has been established that the concentration of shear stresses is realised due to the presence of substantially inhomogeneous deformations in the areas of sharp changes in geometry, a reduction in the radius of the shell (the appearance of edge effects), and in the area of a sharp increase in the radius of the bevel of the shell where external pressure is in place.