A purely torsional dynamic model of multi-stage planetary gear trains is developed to investigate the dynamic characteristics of the transmission system in shield machine cutter drive. In the model,phase difference between mesh stiffness and error among each stage caused by different initial mesh positions is considered,and other factors such as component bearing stiffness,time-varying mesh stiffness and error are considered as well. Inherent characteristic analysis shows there are more unique and diverse vibration modes in multi-stage planetary gear trains than in single-stage planetary gear trains. Through dynamic response analysis,time-domain and frequency-domain response of dynamic meshing force of each stage is obtained. As the frequency of exciting force of medium-speed and high-speed stage is in proximity to the natural frequency of the system,harmonic resonance tends to occur,which needs to be paid great attention to. Dynamic factors of each stage are also computed and prepare the ground for the dynamic optimizing design of planetary gear trains.