The finite-difference technique based on the displacement potential approach of orthotropic composite materials is extended to solve elastic plane stress problems of orthotropic composite materials with geometric perturbations, such as holes, arbitrary defects, notches, etc. In this analysis, one fixed elastic glass/epoxy plate having an internal hole is considered and a uniform shear load is applied to the opposite end of the supporting edge. Critical sections of the plate are identified with the detailed discussions of the elastic field of the plate. Effects of sizes of the holes of the plate on the elastic field are also discussed with the help of graphical solutions. The reliability of the extended finite-difference technique based on the displacement potential approach of orthotropic composite materials is shown by the comparison of solutions between the FDM and FEM.