Abstract: Using a mathematical model for the longitudinal vibration of a drill string and applying harmonic displacement motivation(bit displacement inducing method) and harmonic force motivation(bit force inducing method) to the tri-cone bit at the bottom of a tapered drill string separately, the authors carried on a contrast analysis of the impact of stiffness and installation position of a shock absorber on the maximum axial stress amplitude in the drill pipe and the displacement amplitude at the rotary table. The analysis shows that: the rotary speed-dependent curves of the maximum axial stress amplitude in drill pipe and the rotary speed-dependent curves of the displacement amplitude at the rotary table take the shape of continuous pits, and the speeds between the margins of the pits should be chosen when drilling a well; the shock absorber’s stiffness and installation position have an important influence on the maximum axial stress amplitude in the drill pipe and the displacement amplitude at the rotary table; and the influence of the shock absorber on them is different or even opposite when the tri-cone bit is applied a harmonic displacement motivation and a harmonic force motivation. The bit displacement inducing method should be adopted to study the longitudinal vibration of drill strings. For the future, the damp of the shock absorber should be considered and the downhole measurement should be made to evaluate the role of a shock absorber or develop a new type shock absorber.