In recent years, stochastic finite element (SFE) method undoubtedly has become the most effective and powerful method when analyzing the response moments and structural reliability of large-scale complicated structures with uncertain parameters. And it is well known that the response moments are of main concern for the structural analysis by using SFE method. With conventional perturbation or other SFE method, the computational effort and computer EMS memory requirements are possibly to be too great to be acceptable. For instance, as a conventional SFE method, perturbation method was earlier utilized to evaluate the response moments. With this method, the structural response moments can be evaluated with the first and second moments of random structural parameters taken into account when the structural uncertainties are small or when there are not too many elements in a structure. However, when the number of elements is too great or higher order moments of the uncertain structural parameters are taken into account for the structures with higher degree of uncertainties, the computational cost and computational memory needed by perturbation method can be too huge to be acceptable. Hence, efficient SFE method with high computational efficiency is expected. In 1999, a new analytical method named elementary stiffness matrix decomposition (ESMD) method was proposed by Prof, ER Guokang who proposed some new ideas, i.e., the decomposition of elementary stiffness matrix, and formulated a new solution procedure. Therefore, it is completely different from some conventional methods such as perturbation method and Neumann expansion method. In this thesis, ESMD method is further investigated and applied in the moment evaluation of plane stress problems with Young's modulus being a stochastic field. With this method, the computational cost and the computer EMS memory requirements can be much reduced. 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. In addition, the influence of the fourth moments of structural parameters on the first and second moments of structural responses is also taken into account with high computational efficiency.