A new method for efficient discretization of random fields (i.e., thei
r representation in terms of random variables) is introduced. The effi
ciency of the discretization is measured by the number of random varia
bles required to represent the field with a specified level of accurac
y. The method is based on principles of optimal linear estimation theo
ry. It represents the field as a linear function of nodal random varia
bles and a set of shape functions, which are determined by minimizing
an error variance. Further efficiency is achieved by spectral decompos
ition of the nodal covariance matrix. The new method is found to be mo
re efficient than other existing discretization methods, and more prac
tical than a series expansion method employing the Karhunen-Loeve theo
rem. The method is particularly useful for stochastic finite element s
tudies involving random media, where there is a need to reduce the num
ber of random variables so that the amount of required computations ca
n be reduced.