In order to explore the mechanical response of a deep hydraulic tunnel in orthotropic rock mass，the analytical solutions of a non-circular tunnel under the action of the in-situ stresses and the internal water pressure，are derived. In the process，three polar coordinates are introduced and the conformal transformation method of complex function is adopted，mapping the outer region of the hole in the physical plane to the outer region of the unit circle in the image plane. Then，the stress boundary conditions on the excavation boundary are established. Finally，the stress field is obtained using the power-series method. Taking the inverted U-shaped tunnel as an example，the analytical solutions are verified by the numerical results obtained by ANSYS. The stress distributions along the boundary of a horse hoof-shaped tunnel and a circular tunnel are also analyzed. The results show that，unlike the isotropic rock mass，the stress field for an orthotropic rock mass shows obvious asymmetry. The tangential stresses along the hole boundary increase with the increase of the lateral pressure coefficients except the two corners of the horse hoof-shaped tunnel. Moreover，the internal water pressure can release the tangential stress concentration along the hole boundary，which is more obvious on the regions where the curvature is greater. But great internal pressure may also lead to tensile stress which will affect the stability of the tunnel.