In this paper we investigate the stresses and displacements around an advancing face of a tunnel in an elastic half‐space as well as the induced three‐dimensional ground surface subsidence. An indirect boundary integral formulation for the analysis of tunnels in an elastic half‐space is derived and the half‐space fundamental solution (Mindlin's solution) is adopted to satisfy the traction‐free condition on the ground surface. For the evaluation of the non‐singular integral in the numerical implementation, a simple and efficient algorithm to automatically search for integration orders is developed by basing on the upper bound of error in Gaussian quadrature. Numerical results for some tunnel problems are studied to demonstrate the accuracy and versatility of the proposed method. In addition, the stresses, displacements, and the induced ground surface subsidence for an advancing circular tunnel in an elastic half‐space are calculated and presented in detail.