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Articulated engineering vehicle travels on complex road, its working condition is bad and because of the non-rigid connection between the front and rear body, additional DOF is brought in and the transverse stiffness is relatively weak. When the articulated vehicle runs in a high speed along a straight line, it is easy to cause the transverse swing and the poor handling stability. If it is serious enough, it will lead to "snakelike" instability phenomenon. This kind of instability will increase driving resistance and tire wear, the lateral dynamic load and aggravate the damage of the parts. The vehicle will have a lateral migration of center of gravity (CG) when steering, which will lead a higher probability of rollover accident. A dynamic mathematical model for a 35t articulated truck with four motor-driven wheels was established in this paper, to study the condition for its stable driving and the influence of the vehicle structural parameters.