Using the method of complex functions, we discuss the first fundamental problems of an anisotropic infinite elastic plane weakened by periodic collinear cracks and with periodic boundary loads on both sides of the cracks. This problem was considered by Cai [Engineering Fracture Mechanics 46(1), 133–142 (1993)]. However, the previous method is imperfect. Therefore, the results are incorrect. Here, we revise the method and give a correct solution.