EN 13445 is a European standard that provides rules for the design, fabrication and inspection of pressure vessels. The appendices B and C provide design-by-analysis strategies to analyze pressure vessel design following a stress categorization route and the direct route. The purpose of this thesis is to demonstrate the application of these strategies using the FE-program ANSYS. The tasks in the thesis include the creation of the FE-model of the study object -a pressure vessel with inserted nozzle- development of a meshing strategy and the application of appropiate boundary conditions as well as structural and thermal loads. The computational results shall be interpreted using the aforementioned strategies, which are described in the appendices of EN 13445 after explaining the underlying concepts. The results obtained from the two different analysis methods are to be compared.