An analytical solution was presented for the stresses and displacements around horseshoe-shaped tunnel using Cauchy integral method and Optimization theory in an elastic half-plane. Since the depth of a tunnel was larger than the size of the tunnel, gravity loads were simplified as uniform normal loads along far-field boundary. Finite element model was used to verify the accuracy of analytical solutions. Comparison between the results of numerical analysis by finite element method and those from the closed solutions indicates that the closed solution is reliable and applicable for the stress and displacement field around horseshoe-shaped tunnel tunnels at great depth.