Transport Phenomena in Geomechanics occur under uncertain conditions and their parameters dominated by spatial randomness. The prediction of the progress of these phenomena is a stochastic problem rather than a deterministic. To solve the problem a procedure of conducting Stochastic Finite Element Analysis using Polynomial Chaos is presented. It eliminates the need for a large number of Monte Carlo simulations thus reducing computational time and making stochastic analysis of practical problems feasible. This is achieved by polynomial chaos expansion of the concentration. An example of a pollution development in a soil is presented and the results are compared to those obtained from Random Finite Element Analysis. A close matching of the two is observed.