A bending-torsional coupled dynamics model of the split-torque transmission system is developed based on the theory of the lumped parameter method. The time-varying meshing stiffness, general transmission errors and the backlash are introduced in dynamics model and dynamics equations. Using the Runge-Kutta numerical integral method with varied steps, the dynamical equations are solved. In order to analyze the influence of time-variant and time-invariant supporting stiffness on the vibration characteristics of the system, the model of supporting stiffness of rolling element bearing is introduced. The results show that：the stiffness of the bearing fluctuates at about 4% and the transverse vibration displacement amplitude of the output shaft increases about 5% according to time-variant models. The time-variant characteristic of supporting stiffness enhances the nonlinearity and instability of the system. The time-variant characteristic of supporting stiffness has the larger influence on the dynamic load coefficient of the split torque stages than that of the synthesized torque stages.