The expression of stress function was set up according to the relevant theory of the anisotropic plate

as well as after research of fracture problems about anisotropic composite plate of parabolic crack.Using the conformal mapping method and method of undetermined coefficients

the physical plane with complex geometric crack shapes was mapped into the infinite domain with a unit circle by the appropriate conformal mapping function.Based on the stress boundary conditions

the problems of fracture in composite materials were transformed into the solving boundary value problems of equations and the expression of stress function was determined in the infinite domain.The expressions for stress field and the stress intensity factor are obtained near the parabolic crack tip as well.