Abstract: The concrete lining has viscoelastic properties and permeability. The inner water pressure is partly undertaken by the lining and partly balanced by pore water pressure; it depends on the stress coefficient related to the volume fraction of pore fluid. According to the fluid velocity equality at the interface of lining and soil, and continuity condition of the stress and displacement, the boundary conditions of partially permeability are established. Treating the lining and soil as porous viscoelastic material and two phase medium for liquid-solid respectively, adopting saturated porous medium and viscoelastic theory, this paper developed the analytical expressions for the displacement, stress and pore water pressure of saturated viscoelastic soil subjected to the inner water pressure in the frequency domain, as well as the displacement and stress of lining under the interaction of saturated viscoelastic soil and lining. Parametric study shows that, the stress coefficient and the relative permeability coefficient of the lining and soil have remarkable influence on the system dynamic response. In addition, the inner water pressure undertaken by the boundary lining and pore water can be determined by the stress coefficient.