Based on conformal mapping method of plane elasticity complex function

the analytical solution for non-circular supported tunnel subjected to in-situ stress can be obtained. According to the boundary conditions along the inner boundary of liner and the stress and displacement continuity conditions along the liner-surrounding rock mass interface

the basic equations for solving the analytic functions of the surrounding rock and liner are given. And the stresses and displacements are calculated. In the solving process

support delay and pure bond are taken into consideration. Taking the horseshoe tunnel for example

the tangential stresses of the rock excavation boundary and the contact stresses on the liner-surrounding rock mass interfaces are obtained. The results are compared with that by the ANSYS software. The numerical example shows that the results of two methods are in good agreement.