Abstract: A vertical dynamics model for the three-axle heavy-duty vehicle is firstly established, and the road surface random excitation is generated using the filtered white noise method. Based on a magic formula tire model, a vehicle lateral dynamics model for the three-axle heavy-duty is established. Then a vertical-lateral coupling dynamics model for the three-axle heavy-duty vehicle is established. The vertical dynamical load of the tires is used to couple the vertical dynamics model to the lateral dynamics model. The dynamic coupling vertical-lateral model is implemented in Matlab/Simulink. The simulation results show that the independent vehicle vertical and lateral dynamics model can reflect the ride and handling stability of the vehicle to a certain extent. But the maximum values of the yaw rate, the side-slip angle, and the lateral acceleration of the coupling model are all smaller than those obtained with the independent lateral model. The coupling model for the three-axle heavy-duty vehicle can reflect the impact of the vehicle's vertical motion on the lateral motion. It can be used for the optimization of the vehicle performance under the complex working conditions.