The importance of the detailed analytical proof of fatigue strength of pressure vessel components is steadily growing in order to ensure safe long term operation of chemical plant and power stations. The state of the art is represented by the notch stress oriented concept of the proof of fatigue strength. It is implemented according to increasing quality requirements within pressure vessel codes and guidelines for analysis such as the German AD-Merkblatt S2. The main problem of its practical application is the stress analysis for fatigue including fatigue crack initiating notch stresses. Currently, only numerical instruments of analysis such as the finite elements method (FEM) allow for detailed modelling and analysis according to these needs. General results for standard pressure vessel components such as vessel-to-nozzle connections can be derived from parametric studies based on the finite elements method in case of swelling cyclic loading (start-up and shutdown procedures). These results can be further processed within computer programs enabling the engineer as a user to carry out the detailed proof of fatigue strength for minimum expenditure.