In this paper, the interaction of multiple rows of periodical cracks contained in an infinite elastic plate with far-field stress loaded is studied. An extremely accurate and efficient numerical method fur solving the problem is presented. The method is mainly by means of the crack isolating analysis technique, stress superposition principle, the Chebyshev polynomial expansion of the pseudo-traction as well as the segmental average collocation technique. This method can be used to compute the stress intensity factors of multiple cracks, periodical cracks, and multiple rows of periodical cracks. In the process of dealing with the superposition of interaction of infinite number of periodic cracks, a key series summation technique is used. which aims at numerical results with extremely high accuracy but with less computation work. Many complex computing examples are given in this paper, and, for some typical examples, numerical results are compared with analytic solutions and with previous numerical solutions. For the problem of the one periodical collinear cracks, the accuracy given by this method reaches to 6 significant digits if a/d less than or equal to 0.9 (where a is the half crack length, and d is the half crack spacing). And even if a/d = 0.99, the error is still less than 0.5%. The computer results for multiple rows of periodic collinear and echelon cracks show that the interaction effect between two rows rapidly decline with exponential law as the array pitch increases. This method has tilled the gaps in the research field on the interaction of multiple rows of general periodical cracks.