An approach using complex potentials is presented for analysis of composite plate with an elliptical hole or a rectilinear crack. Composite structure is susceptible to encounter impact damages, which lead to considerable decrease in its residual strength. Such impact damages could be modeled as an equivalent elliptical hole or notch-like crack. Even though finite element method is widely used to analyze stresses or fracture mechanics parameters around such damage, it is tedious to make successive FE-modeling for damage tolerance assessment under fatigue loadings. In this point of view, the solutions based on complex potentials are very simple and easy to use. The computed results are also compared and discussed with those from FEA.