In this study, the efficient analytical method named elementary stiffness matrix decomposition (ESMD) method is further investigated and utilized for the moment evaluation of stochastic plane stress problems in comparison with the conventional perturbation method in stochastic finite element analysis. In order to evaluate the performance of this method, computer programs are written and some numerical results about stochastic plane stress problems are obtained. The numerical analysis shows that the computational efficiency is much increased and the computer EMS memory requirement can be much reduced by using ESMD method.