The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in modern structural mechanics. It is only in recent years that the developments in shastic and deterministic computational mechanics began to be synchronized. To foster these developments, novel computational procedures for the uncertainty assessment of large finite element systems are presented in this monograph. The shastic input is modeled by the so-called Karhunen-Loève expansion, which is formulated in this context both for scalar and vector shastic processes as well as for random fields. Particularly for strongly non-linear structures and systems the direct Monte Carlo simulation technique has proven to be most advantageous as method of solution. The capabilities of the developed procedures are demonstrated by showing some practical applications.