Pressure vessels are used to store fluids under an internal-external pressure differential to the vessel of more than one atmosphere. They are usually designed to withstand internal pressures, but can also be designed to withstand external pressures. They may be subject to pressure and temperature variations, as well as other forms of external loadings. They are used for a wide range of applications, from storing liquids under high pressures (e.g., nuclear power plants) to vessels having to withstand external pressures (e.g., submarine). Pressure vessels have different geometries and sizes, and can be classified as thin-walled or thick-walled. The main types are cylindrical (horizontal or vertical) and spherical, but they may assume other geometries. They may as well have sections with different geometries (such as the VP-CTVP-E-01). First, a static structural analysis is performed, by calculating and comparing the maximum allowable working pressure by Division 1 and 2 of the ASME Boiler and Pressure Vessel Code. In addition it is determined the hydrostatic test pressure (HTP). Then, a complete fatigue analysis is done throughout the structure, both away from discontinuities and at critical points. It is used the theory proposed by the SN Method for that. In order to do so, it is assumed that the vessel will be subjected to cycles of pressure variations. These cycles will induce alternating cyclic and elastic stresses throughout the structure. In the end, the life of the vessel is estimated.