Abstract: Orifice’s boundary conditions of composite material structure are more complex than that of metal material. According to the nonhomogeneous anisotropic elastic and complex function theory, accurate boundary conditions of composite material plate were founded to settle boundary value problems of some complex holes by conformal mapping method. Analytical solutions for composite material plate with circular hole, rectangle hole and hexagon hole are achieved. And then the stress states and its influences on hole-edge stress concentration factors with different hole-shape under external load are discussed.