Based on the strain gradient nonlocal Biot theory， the analytical solution of the dynamic response of the tunnel lining under the action of P-wave is obtained by using the wave function expansion method and the boundary conditions between saturated soil and lining with the deeply buried circular lining as the research object. The influence of non-local parameters and size factors on the dynamic stress concentration factor （DSCF） is investigated for different incident P-wave frequencies. The results show that when the incident wave frequency is low， the non-local parameters and size factor have almost no effect on the DSCF. As the incident wave frequency increases， the effects of the non-local parameters and size factor on the DSCF become more and more obvious. The non-local parameters are negatively correlated with the DSCF， and the size factor is positively correlated with the DSCF.The maximum dynamic stresses in the lining appear on the right side of the lining. With an increase of frequency， the DSCF in the lining shows obvious radial direction and the dynamic stresses in the lining appear in the right side of the lining. The maximum dynamic stresses in the lining all appear on the right side of the lining， With an increase of frequency， the DSCF in the lining shows obvious fluctuation along the radial direction， and the non-local parameters and size factor have little influence on the distribution pattern of the cyclic stresses in the lining.