This monograph presents a stochastic element free Galerkin method for elasto-plastic damage analysis. First and second order perturbation methods are presented to predict the mean and covariance properties of stochastic responses in conjunction with shape function method and Karhunen-Lo?ve expansion method for random field discretization. A novel stochastic state update procedure is presented to solve for the statistics of state variables. Numerical examples are solved to validate the proposed stochastic element free Galerkin method when uncertainty associated with the initial damage is considered. A study also has been carried out in this monograph using the deterministic EFGM to understand the effect of initial damage and its growth on structural response of single and bi- material problems. The newly proposed scaled transformation method developed during course of this research is adopted for the essential boundary and material discontinuity treatment in EFGM. The monograph focuses on the work carried by the first author at Indian Institute of Technology Madras, India; as a part of his doctoral study.