| There are many uncertainties which are normally described as a random function of space in the engineering structure system. In recent years, a new numerical method, stochastic element-free Galerkin method (SFEGM), has bee- n found to be better to study the structure containing the response problem of random variables. The shape function is constructed by Moving Least Squares Method in EFGM, and control equations are produced from the weak form of variational equation. Lagrange multipliers are used to satisfy displacement bou- ndary conditions, and make out numerical solutions. SFEGM can effectively handle structure analysis of related parameters of the randomness and engineer- ing structure reliability. This method simplifies data processing and improves computing speed without grid. And it can solve the problems that can not solve by stochastic finite element method.The paper first expounds some relevant theory of elastic mechanics, the basic control equation (the balance equation, the geometric equations, and the physical equations) of elastic mechanics and the related concept of the stress, strain and the displacement , provides theory basis for solving specific problems in the application of mechanics and exploring stress, strain and node displayce- ment distribution.Secondly, the paper combining SEFGM with small parameter perturbation technology constructs perturbation stochastic element-free Galerkin method (P SEFGM), this method has effectively avoided flaw about the finite element me- thod dividing the grid or reconstructing grid when the processing multiple struc- ture needs. Then, with perturbation stochastic element-free Galerkin method, the paper analysis the reliability of the mix-mode crack with radom variable and rock slide with joints, respectively. From the comparisons of the outcomes of PSEFGM with stochastic finite element method results, this method is proved to be applicable.Finally, a summary of the paper and the future research directions are forecasted.
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