1 Industrial Sectors Interested in Pressure Vessels Pressure vessels are probably the most widespread “machines” within the differentindustrialsectors.Infact,thereisnofactorywithoutpressurevessels, steam boilers, tanks, aulaves, collectors, heat exchangers, pipes, etc. More specifically, pressure vessels represent fundamental components in sectors of enormous industrial importance, such as the nuclear, oil, petrochemical, and chemical sectors. There are periodic international symposia on the problems related to the verification of pressure vessels. FormanyyearsanISOcommitteewasdedicatedtopressurevesselsdesign. There is also a technical committee of the EU specifically assigned to this field. All the industrialized countries have a code relative to pressure vessels design.However,evenwhenthecodeincludesspecificregulationstodetermine the thickness of the different components, typically not all issues facing the designer are discussed. Finally, it is worth noting that a few regulations cause some perplexity. In Italy, a specific area of ISPESL regulations (VSR collection) is devoted to pressure vessels. 2 Current Know-How with Regard to Resistance Verification A pressure vessel is not an easy machinery in terms of resistance verification. A layman can easily make the mistake of considering somewhat simple str- turalformsthatareinfactquitedifficulttoanalyze,especiallyifonewouldlike to apply the most modern criteria of verification (elastoplasticity, self-limiting stresses, etc.). Regardless of the enormous interest in the topic and numerous efforts, many problems have not been studied in-depth, and there is still no agr- ment among scholars and the institutions of the various countries that define VI Preface regulations. In addition, economical reasonsand technical progress constantly present new challenges in connection with new forms and solutions, the necessity to reduce thickness to a minimum, etc.