Abstract: A new stochastic finite element method based on the theory of local average of random fields is proposed. Based on the method, a procedure of computing the reliability index and design point in so called first-order second-moment method for estimation of structural reliability is given. It is shown from the numerical results that the present stochastic finite element method is of the feature of rapid convergence, less C. P. U. time and fewer requirements of input data in comparison with existing stochastic finite element methods.