A complete and accurate method for determining the stresses and displacements of a lined arbitrary shaped tunnel excavated in orthogonal anisotropic rock mass is proposed. The method is based on an analytical method, the complex variable method, and the power series method. The basic equations can be obtained according to the stress boundary conditions along the inner boundary of the lining and the stress and displacement continuity conditions along the lining–rock interface. Based on the method, the tangential stresses along the excavation boundary, the inner and outer boundaries of the lining, and the normal and shear stresses along the lining–rock interface are given. Results show that, when the number of terms of the series is large enough, solutions with high accuracy can be obtained. The positions of the tangential stress concentration, the effect of the displacement release coefficient, and the angle of the rock layers on the tangential stresses along the excavation boundary and both boundaries of the lining are discussed.