Engineering mechanics has been flourishing thanks to modern computers and updated computer codes Today, computational mechanics is able to carry out various structural analyses, provided that the relevant input data are at hand S. Nakagiri (1987).

Recent developments of efficient numerical algorithms for solving general stochastic mechanics problems are based on Monte Carlo simulation, stochastic finite and boundary element, finite differences, stochastic Green functions, and other methods M. Grigoriu (2000).

Actually, the finite element analysis (FEA) is the only tool allowing the analysis of very wide varieties of structures with different complexity levels A. Mohamed, M. Lemaire, J.-C. Mitteau, E. Meister (1998).

The Stochastic Finite Element Codes are, in general, limited to relatively small scatter E. Marchante (1997).

The scientist studies what is, the engineer creates what has never been Th. von Karman.

This monograph is devoted to the finite element method (FEM) in a stochastic setting. However, it appears to be instructive in making some preliminary comments on the deterministic FEM. If we want to go that far, we could mention that the ideas of discretization may apparently be credited to an ancient Chinese mathematician, Zhu Chongzhi, who used an inscribed regular polygon of 3072 sides to approximate the circumference of the circle incidentally approximating ? by the ratio 3927/1250 = 3.1416. If we do not want to go that far, then we may say that the first mathematical hints of the FEM were apparently laid by Hrennikov (1941) and Courant (1943). The term finite element method was coined...