Abstract: On the basis of anisotropic mathematical elasticity, using multiple conformal representation, the stress functions of multiple complex variables for an infinite multiply-connected anisotropic plate are derived. The functions are expanded in the Fourier series on unit circles,and the unknown coefficients of the functions are determined by undetermined coefficients method.Then the stresses in the plate can be calculated.A plate containing multiple elliptical holes or cracks is discussed, and a corresponding FOR-TRAN77 prpgram is developed.Five examples are given.The results show that this method is very effective and convenient.