Abstract: A solution of the stress distribution around a circular hole with a single crack originated from the boundary of hole has been given by complex analysis. Especially, the solution for any orientation of the single crack in an uniaxial or biaxial stress field is able to be obtained by this method. In this method of complex analysis, we used Schwartz integration to derive a mapping function from a circular hole with a single crack at any orientation into a circular hole.According to the equations given in this paper, numerical calculations for five different orientations and four different lengths of the crack have been carried out to obtain the corresponding stress and displacement distributions around a hole. The influence of a single crack originated from the boundary of tunnel on the stress and displacement distribution and fracture of rock around tunnel was analysed by the theory of brittle fracture of rock. Analytical results have shown that the influence of the orientation and position of single crack originated from the boundary of tunnel on the fracture of rock around tunnel is considerable.