To demonstrate the structural integrity of a nuclear pressure vessel, it must be shown that sufficient safety margins exist against brittle and ductile fracture for all parts of the vessel, each being examined under all operational and faulted conditions. In the past, much progress has been made both in establishing analytical and numerical methods in the field of linear elastic fracture mechanics (LEFM) and in the collection of material properties. Thus in principle it is possible to calculate critical and allowable crack sizes for any part of a structure under any loading condition. The analytical methods, however, have been restricted to oneor twodimensional problems only, and the numerical methods require a very detailed evaluation of the stresses and displacements and thus are very costly. For this reason, the safety analysis of the cylindrical parts of the vessel has been well established, whereas more complicated areas such as nozzles have been dealt with in a more limited way or have only been treated in rough approximations. This situation was regarded by many experts as satisfactory, since the cylindrical parts are subject to irradiation and so may exhibit a much more brittle behaviour than the remote nozzle and flange areas. Very recently, however, more interest has been shown in the structural integrity of the nozzle regions.