In this study, a truly meshless method is developed based on the integral form of equilibrium equations. This meshless method is formulated for generalized plane strain assumption with material discontinuity. In the absence of the body forces the domain integration is avoided, and so the computational time of presented method is reduced and presented method computationally is very effective. This method is employed for prediction of the micro-stresses and elastic behavior of the UD Carbon/Epoxy composite. The appropriate boundary conditions are imposed to the representative volume element (RVE) employing a direct interpolation method. The fully bonded fiber-matrix interface is assumed and the continuity of displacement and traction are imposed to the interface. Results revealed that the presented model can provide highly accurate predictions with relatively small number of nodes. Comparison of the CPU time shows that presented model is computationally very effective. Predicted results show excellent agreement with the finite element analysis and available results in the literature.