Shield tunneling machine(STM) is a safety and high-efficiency excavator in the subway tunnel project, but the dynamics of whose multi-stage planetary gearbox is still a critical issue. In this paper, the torsional dynamic model for three-stage planetary gears train(PGT) is developed by lumped parameter method. According to the configuration and design parameters of the planetary gearbox, the natural frequencies are calculated, and the vibration modes are also analyzed. The natural modes can be classified into one of the three categories: rigid-body mode, distinct modes and planet modes. By using finite element(FE) method, the vibration characteristics of gearbox housing are also computed and analyzed for lucubrating vibration transfer and coupling between planetary gears train and housing, which is the important foundation for dynamic optimization of planetary gearbox.