The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in structural mechanics. It is only in recent years that the developments in stochastic and deterministic computational mechanics began to be synchronized. In this monograph novel computational procedures for the uncertainty assessment of large finite element systems are presented. The procedures are applicable to well known problems in computational stochastic mechanics, such as the stability analysis of systems with random imperfections and the dynamic analysis of deterministic systems under stochastic loading. For the dynamic analysis of deterministic systems under stochastic loading, an efficient procedure based on the Karhunen-Loève representation of the response is presented. The capabilities of the developed procedures are demonstrated with several numerical examples.