For the purpose of analyzing the torsional vibration caused by the gravitational unbalance torque arisen in a spindle system when it is machining heavy work piece,a 10-DOF lumped parameter model was made for the machine tool spindle system with geared transmission.By using the elementary method and Runge-Kutta method in Matlab,the eigenvalue problem was solved and the pure torsional vibration responses were obtained and examined.The results show that the spindle system cannot operate in the desired constant rotating speed as far as the gravitational unbalance torque is engaged,so it may cause bad effect on machining accuracy.And the torsional vibration increases infinitely near the resonant frequencies,so the spindle system cannot operate normally during these spindle speed ranges. For the purpose of analyzing the torsional vibration caused by the gravitational unbalance torque arisen in a spindle system when it is machining heavy work piece, a 10-DOF lumped parameter model was made for the machine tool spindle system with geared transmission. By using the elementary method and Runge-Kutta method in solved, the eigenvalue problem was solved and the pure torsional vibration responses were obtained and examined. The results show that the spindle system can not operate in the desired constant rotating speed as far as the gravitational unbalance torque is engaged, so it may cause bad effect on machining accuracy. And the torsional vibration increases infinitely near the resonant frequencies, so the spindle system can not operate normally during these spindle speed ranges.