Abstract: The classical solution for a single circular cavity in an infinite elastic medium has been used as the basis for many investigations in engineering practice. However, the problem of an elastic half plane with a circular cavity is still not perfect. Using Verruijt’s conformal mapping function, the region of exclusion of a hole in a half plane was transferred into a unit annular domain. Then the analytic functions could be expanded as Laurent series in this region. The coefficients in the Laurent series were determined by means of the boundary conditions as well as the requirement of convergence of the series. Furthermore, it could be obtained the stress and displacement fields of an elastic half plane with a circular cavity, loaded arbitrarily on the horizontal boundary. As an example, a specific subway tunnel was analyzed by this method eventually.