Abstract: In the past, when employing the plane elastic complex variable method for the mechanical analysis of non-circular tunnels with lining support, the conventional approach involved conformally mapping the outer region of the tunnel to the outer region of the unit circle on the image plane. Additionally, the same mapping function was utilized to map the lining section to the circular area on the image plane. However, this method resulted in non-uniform thickness of the lining, especially when the lining was relatively thick, causing significant distortion in the section shape of the lining. To address this issue, this paper introduces two mapping functions to separately map the outer domain of the cavity and the section of the lining to the outer domain of the unit circle and a circular area on the image plane, respectively. This approach is adaptable to different lining thicknesses, ensuring relatively uniform lining thickness, particularly in cases of thicker linings. The traditional power series method is replaced with the boundary collocation method in solving the analytical functions. This method combines the two sets of mapping functions to obtain stress and displacement solutions for the problem. Using the horseshoe tunnel as an example, the solution results align well with the numerical solution obtained by ANSYS. The paper analyzes the influence of lining thickness on tunnel stress and displacement. With the solutions presented in this paper, the preliminary design of a tunnel under similar conditions can be carried out conveniently and quickly.