Abstract: In this paper are given the solutions of the periodic crack problems of infinitive anisotropic medium for plane symmetric loadings by means of the method of complex function. There problems are now reduced to the determination of two complex functions that must satisfy certain boundary condition on the periodic cracks. The stresses,the displacements and the boundary conditions are assumed to be periodic, and further, the stresses are assumed to be bounded at infinity. The solutions are expressed in closed forms.