Trucks are one of the most common modes of transport and they are operated in various road conditions. As a rule, all-wheel drive trucks are equipped with special systems and mechanisms to improve their off-road capability and overall efficiency. The usage of blocked mechanisms for power distribution is one of the most popular and effective ways to improve the off-road vehicle performance. However, the lock of differential may adversely affect the stability and control of vehicle because of the unobvious redistribution of reactions acting on wheels, which consequently leads to poor performance and safety properties. Problems of rational distribution of power in transmissions of all-wheel drive vehicles, as well as research in the field of improving directional stability and active safety systems are among the priorities in modern automotive industry. To study dynamics of a vehicle with wheel formula 6x6 a mathematical model of the vehicle was developed in an environment of LMS Amesim software package. The model includes the realization of the features of all major mechanical units of a vehicle: engine, transmission, suspension, drive wheels. Besides, the model takes into account the so called "external" dynamics of the vehicle and includes interaction of the wheels and pavement and implementation of possible changes in environmental conditions. With help of the mathematical model we have managed to estimate the trajectory and directional stability of all-wheel drive trucks with lockable differentials for different operating conditions. The results allowed us to develop the most effective, in terms of stability and control, algorithm for control of the power distribution system.