Cylindrical pressure vessels subjected to pressure and temperature has been widely studied. This book presents the review of the work related to thermal stress and thermo mechanical stress distribution in thick cylinder pressure vessel and multilayered composite pressure vessel subjected to either thermal load only or both thermal and pressure load. Papers related to stress distribution in fiber reinforced composite and filament wound composite vessel are also included in the book. The application of finite element method in solving the problems related to thermal and thermo mechanical stresses are discussed in this book. The temperature distribution for steady state and transient condition are also studied. The study of thermo elastic stresses in pressure vessel find wide application in the design of advanced engineering structures.