In recent years, the fundamental research on the structural strength and optimal deisgn of composite pressure vessel and piping under complex load and environment has become crucial to ensure safe, economical and reliable run of these structures in area of advanced energy utilization. The content of this book includes the strength prediction of composite vessel using composite laminate theory and finite element analysis, the optimal design using adaptive genetic algorithm and immune algorithm as well as the failure analysis under deflection load and the fatigue lifetime evaluation under cyclic vibrating load using finite element analysis for buried piping. Specially, the authors attempt to explain some physical phenomena such as the stiffness degradation in process of damage evolution for composites. In addition, some advanced methods for predicting the collapse failure of these structures using finite element analysis are also discussed. This book may provide a good reference available for the mechanical strength prediction and optimization of other complex structures.