One of the authors have developed the first-order perturbation based stochastic homogenization (FPSH) method to predict the macroscopic properties considering the geometrical and physical uncertainties at the microscale. The feature of our formulation lies in the use of many physical random parameters, whose verification is shown in this paper by comparison with Monte Carlo simulation using 10,000 sampling points. This method is extended in this paper to predict the microscoipc strain when the RVE (representative volume element) model is under given macroscopic strain condition. This enabled us to predict the damage occurance and also the damage propagation in a stochastic way. Many examples are included in this paper. First, the parameterization of the geometrical uncertainty is described for a GFRP woven fabric reinforced laminate. The idea was extended to a 3D woven ceramic matrix composites and initial damage occurance in the fiber bundles was predicted. Finally, a demonstrative example of a RVE model with single short fiber is presented to show the stochastic prediction of damage propagation in the interphase between fiber and matrix.