The topic of this paper is the numerical analysis of the fermentation tank for beer production. At the beginning of the paper, a brief introduction was presented on the production of beer and fermentation tanks. Analytical and numerical calculations were performed for the selected tank with a usable volume of 1000 l and a total volume of 1200 l. The geometry of the selected tank consists of one conical, one spherical and two cylindrical shell and a thin circular plate. Before the calculation, a brief theoretical introduction on thin circular plates and shells and on the finite element method (FEM) was presented. Analytical calculation was performed using equations derived from the theory of thin circular plates and shells. Radial displacements and rotations were determined for each part of the tank and shown in the diagram. Also, stresses were determined at critical places of the tank. By applying Tresca’s failure theory, equivalent stresses were determined at these places, and based on the highest stress obtained, the strength of the tank was examined in relation to the elastic limit of the selected tank material. Numerical calculation was performed using the Abaqus® software package based on the finite element method (FEM). Verification of finite elements for this analysis was made on the example of one cylindrical shell loaded with constant pressure. Different types of finite elements and different mesh densities show the convergence of solutions, thus justifying the use of finite elements for the main calculation. By applying main calculation radial displacements and rotations were determined for each part of the tank as well as the equivalent stresses at critical places. Radial displacements and rotations are shown in diagrams and graphically throughout the tank and in a more detailed view near the joints. Equivalent stresses were determined using Tresca’s and von Mises failure theory and are shown graphically throughout the tank and in more detailed view for each critical place. For the highest stress obtained by Tresca’s failure theory, the strength of the tank in relation to the elastic limit of the selected tank material was examined. The results obtained using both methods were compared. Radial displacements and rotations are compared in overlapping diagrams and the equivalent stresses obtained by applying Tresca’s failure theory are compared by the means of table and the relative error of the numerical solution is shown.