Considering the compression of medium and fluid

coupled vibration of saturated fractional derivative type viscoelastic soil and a circular tunnel with partially sealed shell lining in the frequency domain is investigated according to theories of Biot and elastic shell. The stress and displacement constitutive behavior of the soil skeleton is described by fractional derivative model which reflects the rheological properties of the medium while regarding soil as a liquid-solid saturated porous medium. The expressions of displacement

stress and pore water pressure are obtained while the inner boundary of circular tunnel is subjected to axially symmetric radial traction and axially symmetric fluid pressure respectively by introducing a partially permeable boundary condition. With the parameter analysis

it is revealed that the order of fractional derivative model on the responses for the system subjected to the symmetric radial traction is much greater than that of the system under the axially symmetric fluid pressure. And resonance phenomenon occurs obviously. Nevertheless the system responses do not have remarkable resonance phenomenon under axially symmetric fluid pressure.