Abstract: Abstract: With the increase of the speed of high-power tractors, the tractor's vibration problem has become more and more prominent in recent years, since tractors often travel on rugged roads. High-power tractors mostly work with farm implements hung by hydraulic hitch system. The hanging farm implements are raised to the highest point in transit. When the tractor is travelling on the rugged road, the vibration of the tractor with a farm implement will be more intense for the existence of the hanging farm implement sometimes would bring a great pitch vibration. This paper discussed the effect of the existence of the farm implement on the vibration characteristics of the tractor. For the first time, the movement and stress distribution of the hitch system and the farm implements were analyzed in detail, besides that of the tractor's body. The mathematical vibration model of the tractor with a farm implement was established. And then the incentive mathematical model of the concrete barriers was established and the process of the tractor driving over obstacles was simulated with the Matlab based on the mathematical model. Variation curves of each key point were got and some conclusions were obtained by the simulation. The front tire's dynamic load and dynamic load coefficient increased significantly because of the existence of the farm implement. The front tire's dynamic load coefficient increased from 0.26 to 0.55, which seriously affected the safety of the driving. When the tractor encountered obstacles, low frequency vibration had obviously been strengthened. In both cases of load and no-load, the first vibration mode of the tractor was the body's vertical vibration, and the second vibration mode of the tractor was the body's pitch vibration. Without the farm implement, the tractor's vertical vibration frequency was 3 Hz, and it became 2.5 Hz with the farm implement. In case of no-load, the tractor's pitch vibration was hardly apparent. When the farm implement was hung up, the tractor's pitch vibration was significantly enhanced by the farm implement, and the frequency of that was 4.8 Hz. Because of the nonlinear coupling between the vibration of the tractor and the motion of the hitch system, the third vibration mode appeared under certain conditions, the frequency of which was between 10 and 15 Hz. Both the performances of the second and the third vibration mode of the tractor with farm implement would be harmful to the driver's comfort and the safety of the tractor. The vibration of the farm implement made the force of the lower pull rod's hinge point of the electro-hydraulic hitch system changed correspondingly. There was a good linear relationship between the vertical component of the force and the vertical acceleration of the farm implement's centroid. Therefore, we could use the vertical force instead of the acceleration to represent the vibrational state of the tractor when we designed the active vibration control system of the tractors later on. The simulation results agreed well with the experimental results, which verified the correctness of the mathematical model. The methodology and conclusion provide a theoretical basis for the tractor vibration control.