The analytic solutions for the dynamic response of a circular lined tunnel with an imperfect interface subjected to a cylindrical P-wave were presented in the paper. The wave function expansion method was used and the imperfect interface was modeled with a spring model. The interface separating the liner from the surrounding rock was considered to be homogeneous imperfect. The dynamic stress concentration factors (DSCF) of the rock and liner were evaluated and discussed. The effects of incident wave’s frequency, bonding conditions and distance between the wave source and the tunnel were examined. The results showed that the low-frequency incident wave leads to a higher DSCF than the high-frequency incident wave. The bonding conditions have a great effect on the dynamic response of the lined tunnel. When the bond is extremely weak, the resonance scattering phenomenon can be observed. When the distance between the wave source and the tunnel, depending on frequency of the incident wave, is considered as large, the cylindrical wave can be treated as a plane wave. Limiting cases were considered and good agreement with the solutions available in the literature was obtained.