Abstract: In this paper, by the method of conformal mapping, the region with a hole in transformed into the inter-nal region of a unit circle,and the boundary of the hole into a circle. Then by applying the method of complex func-tion in elasticity,the stresses in the region with the hole can be solved under the three stress fields far from theholes In the paper, the stress concentrations of U-shaped holes and ladder-shaped holes have been solved Thestress results may be used as reference when these kinds of holes are installed in engineering structures.