Due to the fact that in urban rail transit, elastic wheels, as the main load-bearing components of trains, play a great role in vibration reduction and noise reduction; in view of a further inquiry into the advantages of a certain type of elastic wheel in vibration reduction and noise reduction compared to rigid wheels, and on the basis of the elastic wheel modelling method and the study of the ontological model of rubber materials in the elastic wheels, a finite element model of elastic wheels and rigid wheels has thus been established by using Hypermesh software. Based on the Optistruct module, a simulation analysis has been made of the dynamic stiffness of elastic and rigid wheels, thus obtaining the speed and acceleration frequency response curves of both at the same test point. The results show that elastic wheels have significant vibration reduction effects in the high-frequency range. In addition, a prediction has been made of the fatigue life of this type of elastic wheel under random vibration conditions by using Ansys software. After an analysis of the equivalent stress distribution cloud map and fatigue life distribution cloud map of the wheel, dimensional improvements are made to the stress concentration areas of the elastic wheel, with the results showing that the fatigue life of the improved elastic wheel is characterized with a significant improvement.