Tanks are storage vessels for liquids. They can have different appearances; some are short and wide, others are tall and slim, some are small, others are large. In this thesis a tank of 6 m in both diameter and height has been used to obtain numerical results of the stresses in the tank. Tanks are most often thin-walled with stepwise variable shell thickness with thicker wall sections at the bottom of the tank and thinner at the top. Since they are thin-walled they are susceptible to buckling and there are conditions the shell construction must meet. The conditions that has to be met are determined by the laws and regulations that govern tank design. The National Board of Housing, Building and Planning (Boverket) is the new Swedish authority for rules of tank design and the Eurocodes are the new family of standards that should be followed. Sweco Industry AB is the outsourcer of this thesis and wants to clarify what rules that apply now when the Eurocodes are to be followed. The thesis project has produced a calculation document in Mathcad for tank shell design according to the Eurocodes with stress calculations according to membrane theory and linear elastic shell analysis. This thesis has also produced a comparison of stresses calculated using membrane theory, linear elastic shell analysis and finite element method (FEM). The comparison has been made for numerical results given for an arbitrarily designed tank wall. The loads acting on the tank included in the description were self-weight, internal and hydrostatic pressure as well as wind and snow loads. The loads were described in accordance with the Eurocodes. Some assumptions had to be made where the standard was vague or deficient in order to make calculations by hand possible. For example, the wind load had to be described as an axisymmetrically distributed load rather than an angularly varying. The stresses in the tank wall were calculated through creating free-body diagrams and declaring equations for force and moment equilibrium. The loads and boundary conditions were set in a corresponding manner in the FEM software Ansys as in the calculation document in order to obtain comparable results. When compared, the stress results calculated with membrane theory and FEM were quite similar while the stresses calculated with linear analysis were a lot larger. The bending moments were assumed to be too large which make the results of the linear analysis dominated by the moments. The arbitrarily dimensions set for the tank did thus not fullfill the conditions when linear analysis was used but did so for membrane theory and FE-analysis. Since the results calculated with membrane theory were very close to FEM in most cases, even without expressions for local buckling, it was assumed to be an adequate method in this application. Expressions for local buckling are although needed for the meridional normal stress. The conclusions of the results obtained are that membrane theory is a simple and adequate method in most cases. Linear analysis thus becomes redundant since it is more complicated and more easily leads to faulty results. Furthermore it cannot be used for higher consequence classes than membrane theory. FEM, with a computer software such as Ansys, is although the most usable calculation method since it can conduct more complicated calculations and is allowed to be used for all consequence classes.