With the increase in the demand for a rational treatment for uncertainty in geotechnical engineering, the use of probabilistic method has gained importance. Recent developments in reliability theory provide a way of quantifying uncertainties and handling them consistently. Stochastic finite element approaches combine well known deterministic finite element analysis with reliability methods to produce more rational design. In the present study, direct computation of the covariance matrices and solution for the variances in the finite element analysis of single pile by first order second moment methods (FOSM) has been investigated. The problems of a pile subjected to lateral load and axial load have been considered. In this study, the pile modulus is assumed to be deterministic whereas the soil modulus is considered as a random variable. Results indicated that correlation between displacements exist even if the element properties themselves were mutually independent.