Abstract: Many types of engineering contain structures with holes, which stress concentration occurs inevitably at the hole edge under external loads. To ensure the safety and stability of the structure, it is of great practical value to accurately derive the stress distribution of the perforated structure. At present, most researches are involved with single hole and double special shaped holes with analytical solution, while there is little research on two arbitrarily shaped holes. Complex variable method is applicable to two arbitrary holes if the corresponding mapping function could be found. A general form of mapping function is proposed that could conformally map arbitrary infinite doubly connected domain into a concentric ring, and the mapping function is found by optimization method. Concerning the problem of an infinite plate with two arbitrarily shaped holes, the stress boundary conditions are established based on complex potential theory. The problem is transformed into concentric ring domain by the mapping function and the two analytical functions are transformed into Laurant series simultaneously which is solved by power series method. The analytical stress solution is compared with the ANSYS numerical solution. The effects of load and distance on the stress on the boundary is investigated by the present method.