Urban rail transit lines have high requirements for vibration reduction performance in special sections such as small radius curves and acceleration and deceleration. Additional rail vibration absorbers are an effective method to suppress track system vibration. For the purpose of suppressing the vibration of the rail in special sections of the subway, the vertical dynamic model of the rail with additional rail vibration absorber is established and the vibration response of the rail is solved. Based on the analysis of the vibration form of the rail, a Pinned-Pinned vibration mutation index and grading standards for evaluating its vibration are presented. The design method for suppressing rail vibration by a single rail vibration absorber is proposed and the optimized design frequency expression is fitted. The adverse effects of the additional rail vibration absorber are pointed out. Furthermore, the design method of the double rail vibration absorber is proposed. The results show that the rail receptance occurs a mutation phenomenon which expressed as peaks and valleys between 900-1 300 Hz. The established mutation index can be used to evaluate the Pinned-Pinned vibration of the rail. The single rail absorber can effectively restrain the rail vibration. However, the additional vibration absorber will adversely affect the track system, resulting in an increase in the force of the wheel rail. The double rail vibration absorber has the characteristics of two damping frequencies, which can not only effectively suppress the rail vibration, but also the adverse effects on the rails are small, making the vibration response of the rails more gradual. The work of the study has important reference value for the quantitative evaluation of the Pinned-Pinned vibration of the rail and the theoretical parameter design of the rail absorber. © 2020 Journal of Mechanical Engineering.