An analytical procedure was presented to evaluate the dynamic stability of circular tunnel linings subjected to radial harmonic stresses. Considering the dynamic interaction between the linings and the surrounding soil, the calculation of critical exciting frequency of linings was derived. A parametric study was performed to investigate the effects of some key parameters of the linings -soil system on the dynamic stability of the circular linings, such as the foundation's properties, ratio of the lining's radius and thickness, the exciting stresses, and the damp of the system.Numerical results demonstrate that the properties of the surrounding soil and the damp of the soil -lining system barely affect the dynamic stability of the lining.Whereas, the thickness of the lining and the input exitation have a considerable influence on the dynamic instable area of the lining.