As modern structures require more critical and complex designs, the need for accurate and efficient approaches to assess uncertainties in loads, geometry, material properties, manufacturing processes and operational environments has increased significantly. Reliability assessment techniques help to develop initial guidance for robust designs. They also can be used to identify where significant contributors of uncertainty occur in structural systems or where further research, testing and quality control could increase the safety and efficiency of the structure. This book provides engineers intuitive appreciation for probability theory, statistic methods, and reliability analysis methods, including Monte Carlo Sampling, Latin Hypercube Sampling, First and Second-order Reliability Methods, Stochastic Finite Element Method, and Stochastic Optimization. In addition, this book explains how to use stochastic expansions, including Polynomial Chaos Expansion and Karhunen-Loeve Expansion, for the optimization and the reliability analysis of practical engineering problems. Example problems are presented for demonstrating the application of theoretical formulations using truss, beam and plate structures. Several practical engineering applications, e.g., an uninhabited joined-wing aircraft and a supercavitating torpedo, are also presented to demonstrate the effectiveness of these methods on large-scale physical systems.