The article presents investigation of deformations of a metal-composite pressure vessel with a thin-walled steel liner. The study includes the problem of liner wrinkling during the manufacture and operation of such vessels using the example of heating a contact-constrained ring. The cylindrical part of the vessel was taken as the design scheme. A 3D finite element model was built for it, taking into account the unilateral constraint of the liner and the shell on the contact surface. The increase in the temperature of the ring with time was taken into account. Analysis of structural deformation was performed according to the methodology of dynamic analysis. The calculations were carried out in the LS-DYNA software package in a dynamic formulation. Comparison of the obtained results of calculations with the data of the experiment known from the literature showed a good agreement, which indicated a high accuracy of the calculation, and, consequently, applicability in practice. The proposed approach makes it possible to evaluate the bearing capacity of contact-constrained shell structures already at the design stage.