As modern structures require more critical and complex designs, the need for accurate ways to assess uncertainties in loads, geometry, material properties, manufacturing processes and operational environments has increased. Reliability assessment techniques help to develop safe designs and identify where contributors of uncertainty occur in structural systems. This book provides readers with an understanding of the fundamentals and applications of structural reliability, stochastic finite element method, reliability analysis via stochastic expansion, and optimization under uncertainty. Probability theory, statistic methods, and reliability analysis methods are discussed. In addition, the use of stochastic expansions for the reliability analysis of practical engineering problems is also examined throught the use of examples of practical engineering applications. This book will be of value to graduates and post graduates studying in this field as well as engineers, researchers, and technical managers.