The aim of this work is to conduct a control numerical analysis of stresses and strains in the existing structural design for a refillable steel liquid gas tank. The numerical analysis of strength was carried out in the computer program package Abaqus, which is based on The Finite Element Methods. In the introduction, the given problem is described and the pressure vessel is shown. In addition, the concept of liquefied petroleum gas is elaborated. In the second chapter, the Finite Element Method and the computer program Abaqus are described. Certain types of finite elements used in this assignment are further elaborated. Techniques of merging different types of finite elements, which are applied in the final analysis, are described. In the third chapter, through simple examples for which the analytical solution is known, the effectiveness of individual finite elements is computed, as well as the selection of suitable modeling techniques, and the accuracy of merging techniques of different types of finite elements was tested. In the fourth chapter, the process of numerical calculation of the given gas tank is presented. The discussion focused on two numerical models, a three-dimensional model and a simplified axisymmetric model. The results for stresses and displacements in the tank and the mutual comparison of the mentioned models are shown. Furthermore, some of the details that make this analysis even closer to reality are discussed.