In order to motivate the incorporation of reliability concepts in the structural design and analysis procedures, the engineering community is in need of finite element (FE) software with capabilities of including the stochastic nature of input parameters. This book focuses on the modeling of uncertainties in structural systems and on strategies for the reliability assessment of structures analyzed by FE programs. Concepts are introduced for the numerical treatment of spatially varied uncertain quantities through the discretization of the relevant random fields as well as for robust and efficient finite element reliability analysis and updating of the reliability in light of new information. The presented reliability methods are termed non-intrusive, since they can be programmed in a stand alone fashion without requiring access to the core routines of the FE software.