In mining engineering a large number of stability problems of layered rock mass is are often encountered.Layered rock mass is generally considered to be transversely isotropic solid in mechanics.Based on the equilibrium equations,generalized Hooke’s law equations and geometry equations of transversely isotropic elasticity mechanics,compatibility equation of plane strain of transversely isotropic body is deduced.Based on the complex variable expression of stress function,the complex variable expression of displacement components of transversely isotropic plane strain problem is deduced.Finally the displacement analytic solution of a deep tunnel with arbitrary cross section in transversely isotropic rock mass is derived by conformal mapping method.Although the cross section of the tunnel is assumed to be parallel to the isotropic plane in the deduction,the displacement analytic solution indicates that radial displacement of surrounding rock is related not only to elastic modulus and poisson ratio on the isotropic plane but also to that in the direction normal to the isotropic plane.