Wheel faults are the main causes of safety issues in railway vehicles. The modeling and analysis of wheel faults is crucial for determining and studying the dynamic characteristics of railway vehicles under variable speed conditions. Hence, a vehicle–track coupled dynamics model was established for analysis and calculations. The results showed that the dynamic features of the wheel with a flat fault were more pronounced under traction and braking conditions, whereas the variations in the features under coasting conditions were insignificant. In this paper, a short-time fast Fourier transform and reassignment method was used to process the signals, because the results were unclear when the time–frequency graph was processed only by short time Fourier transform, especially under braking conditions. The variation in the fault frequency under variable speed conditions was determined. Finally, statistical indicators were used to describe the vibration behaviors caused by the wheel flat fault.