In this paper, the stress and strain of cylindrical pressure vessels are analyzed. Different cases were obtained by selecting different models of cylindrical vessels that are most commonly encountered in practical applications. A detailed analysis and comparison of theoretical and numerical results for the cases when the cylindrical vessel is loaded with internal pressure was performed. Also, the influence of the thermal load on the distribution of characteristic stresses an deformation is given. Analytical solutions were obtained on the basis of the classical theory for infinitely long elastic tubes of finite wall thickness and in the case of the plane state of deformation. Special attention is dedicated to the analysis of stresses and strains in the vicinity of joints (caps). For real world models, approximate numerical solutions were obtained using Solidworks application and adequate FEM procedure. The comparison of results and presentation of solutions is given graphically in the form of diagrams and corresponding 3D models.