Abstract: The state of vibration for drillstrings and the cause of vibration are described in this paper. For the problem of longitudinal vibration, mathematical models are established for the force and displacement excitation methods, respectively. The calculation results indicate that the rotation velocity of anti-vibration by force excitation method is in opposite to that by displacement excitation method. The rotational velocity of anti-vibration by force excitation method is just the resonant rotational velocity by displacement excitation method, and vice versa. Traditionally, to study the frequency response of longitudinal vibration for drillstring, the force excitation is applied to the boundary condition, which is used to guide the operation of anti-vibration on site. Thus, it provides the best anti-vibration rotation velocity, which is just the resonant rotational velocity. In the operation, since the longitudinal jump of drills is much stable than the variation of the force and the dynamic force is more important than the dynamic displacement, the displacement excitation method should be used to study the longitudinal vibration for drillstrings. For the problem of torsion vibration of drillstring, the mathematical model of torsion moment excitation method and rotational angle excitation method are established, respectively. It is concluded that the rotational angle excitation method should be used to study the torsion vibration of drillstrings.10 Yigit, A S, Christoforou A P. Coupled torsional and bending vibrations of actively controlled drillstringsJ. Journal of Sound and Vibration, 2000, 234(1): 67-83.11 刘清友, 马德坤, 钟青. 钻柱扭转振动模型的建立及 求解J. 石油学报, 2000, 21(2):78-82. Liu Qingyou, Ma Dekun, Zhong Qing. A drilling string torsional vibration model and its solution J. Acta Petrolei Sinica, 2000, 21(2): 78-82. (in Chinese)12 Raymond David W, Elsayed M A. Analysis of coupling between axial and torsional vibration in a compliant