This paper presents a procedure of conducting Stochastic Finite Element Analysis using Polynomial Chaos. 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 displacement field. An example of a plane-strain strip load on a semi-infinite elastic foundation is presented and results of settlement are compared to those obtained from Random Finite Element Analysis. A close matching of the two is observed.