A dynamic track stabiliser vehicle is an unconventional vehicle for maintaining the quality of ballasted tracks, and its dynamic performance has a significant impact on its working efficiency. For the first time, this paper proposes a comprehensive dynamic track stabiliser vehicle–track coupled vertical and lateral multi-body dynamics model based on classical vehicle–track coupling dynamics theory. In this model, detailed attention is given to the vertical, lateral, roll, yaw, and pitch motions of the components, including the vehicle body, bogies, wheelsets and stabilisers. The Shen–Hedrick–Elkins theory is employed to describe non-linear wheel–rail contact relationships between the bogie wheelsets and the rails, and three various methodologies are adopted to address complicated wheel–rail interaction problems between the stabiliser wheelsets and the rails. This comprehensive multi-body dynamics model enables a detailed investigation of the dynamic performance of the system under complex excitations, such as the lateral excitation of the stabilisers and vertical downward pressure exerted by hydraulic cylinders, especially the dynamic response of the stabilisers in the vibration environment of the complete vehicle. The dynamics model was fully validated by comparing its results with time- and frequency-domain data obtained from field tests. The results indicate that the model is capable of being used for analysis of the dynamic performance of dynamic track stabiliser vehicles.