By establishing a cellular rail model based on the spectral element method and combining with Bloch theorem, the vertical decay rate of the rail using the egg fastening system is studied, based on which, the influence of tuned rail damper (TRD) on the vertical decay rate of the rail is analyzed. The results show that the vibration characteristics of the egg fastening system itself causes a new peak of the rail vertical decay rate of around 500 Hz. The influence of the change of the parameters of the iron pad and the rail pad on the vertical decay rate of the rail is mainly reflected at a high frequency of above 500 Hz, and the influence of the change of the parameters of the egg fastening system on the vertical decay rate of the rail is mainly reflected at a middle and low frequency of below 400 Hz.TRD can greatly increase the vertical decay rate of the rail in the vicinity of its working frequency (depending on the mass and stiffness of TRD). The vertical decay rate of rail in the range of 200 to 400 Hz with TRD is more than five times larger than that without TRD. Increasing TRD damping can increase the decay rate of the rail.