Gas pressure tanks are closed containers that are used for storing gases or liquids that are under pressure which is substantially different from the enviromental one. Today they represent one of the most important forms of stored energy. Due to the very high pressures inside the tank there is a high level of strength safety and stiffness of the constructions themselves. Prior to the calculation of the pressure vessel numerical methods used in the analysis are explained. Additionally, finite elements which were used in verification examples and in the analysis of the tank were briefly described. After that the techniques that we use in the detailed analysis of local structural parts were explained. In the first verification example the triangular and rectangular shell elements of the first and second degree were compared while studying the convergence of their solutions based on the previously computed analytical solution for rectangular plate loaded with surface pressure. In the second verification task the analytical solution for the water tank was compared with the solutions that had been obtained by numerical analysis through the use of shell elements, 3D elements and the submodeling technique. The third verification example consists of the analysis of the pressure vessel while comparing the analytical solution with the solutions obtained through the use of shell elements and the submodeling technique. Analysis of the horizontal tank begins with the analytical assignment of the necessary shell thickness. The model of the container is made by using the shell quadrilateral elements of the second order which is needed to perform an analysis of the before computed thickness. The thickness is varied according to the strength condtioin. Except to the thickness, other dimensions are changed in order to obtain the needed strength of the construction. After that, the reinforcements are set on the critical places and by using the submodeling technique their strength is verified. Furthermore, it is necessary to specify the dimensions of the supports that are verified by using hexagonal prismatic elements of the second degree and, if necessary, they are changed until their strength is satisfied. Finally, by using the shell and 3D elements joining technique ("Shell to solid coupling"), the strength of the connection of the tank and the tank itself is verified. All of the numerical procedures are iterative and they are performed until the dimensions that satisfy the strength condition are obtained.