Stochastic finite element (SFE) method undoubtedly has become a powerful tool for the response analysis of large-scale complicated structures containing uncertain parameters since being proposed three decades ago. With SFE method, the resulting random algebraic equations need to be solved. Currently the moments of structural responses, such as mean values and variances, can be obtained from the random algebraic equations. In order to obtain the response moments, a few techniques were utilized for the response moment evaluation such as perturbation method which, at the moment, is popularly employed for calculating the first and second moments of structural responses. The computational effort and computer memory needed by perturbation method is huge for large-scale structures even if only the second moments of random structural parameters are taken into account. In 1999, a completely new methodology named elementary stiffness matrix decomposition (ESMD) method was proposed by Er and Iu and it was proved that the computational effort needed by ESMD method can be greatly reduced compared to perturbation method. The idea of ESMD method is completely different from the conventional methods for structural analysis. It is based on the decomposition of elementary stiffness matrix into several basic elementary stiffness matrices with single rank. In 1998, EPM method for multi-parameter PDF estimation of random variables was proposed by Er. It was proved that the PDFs obtained using the EPM method converge to those obtained from MCS as the number of parameters in the approximate PDF increases. The following work has been done in this thesis. (1) The ESMD method is employed to analyze the stochastic plane frames and stochastic space frames, to further show its efficiency in analyzing stochastic frames with comparison to the computational efficiency of perturbation method. The mean values and variances of structural responses are obtained with both ESMD method and perturbation method. Numerical results are obtained to show that the relative computational effort needed by ESMD method decreases linearly as the number of elements increases compared to the computational effort needed by perturbation method if only the second order moments of structural random parameters are taken into account. (2) The fourth order moments are taken into account and show that the relative computational effort needed by ESMD method can decrease quadratically as the number of elements increases. (3) With ESMD method, numerical results obtained with second order moments and with fourth order moments of random structural parameters being taken into account, respectively, are compared with those from Monte Carlo simulation to show the improvement with fourth order moments being considered. (4) The EPM method and MCS are combined and employed to estimate the PDFs of random variables in stochastic plane frames. Numerical results show that the PDFs obtained with the combination of EPM method and MCS converge to those conventional MCS with only few samples. So the computational effort needed with the combination of EPM method and MCS can be greatly reduced.