Abstract: Using the conformal mapping,the region of exclusion of a hole in a half plane was tansfered into a cirque.Then the analytic functions could be expanded as Laurent seriers in this region.The stresses and displacements under given displacement could be solved by the complex method founded by Muskhelishvili.The influence of the displacements due to different depth and different Poisson’s ratio was discussed,and the influence of the stresses due to different depth was discussed too.It was shown that the exact solutions of the third boundary condition suggested by the author was important in the designing of shield tunnling after the comparision of the solutions under four different conditions with the data observed in five different tunnels.