Problem. The distribution of normal reactions between the axles of a wheeled vehicle when braking is a very important parameter that determines the so-called curves of the realized tire traction. International requirements for the braking of wheeled vehicles uniquely determine the method of calculating the curves of the realize tire traction for a two-axle vehicle. At the same time, multi-axle vehicles with the so-called "balancing trolley" have become widespread in the world of automotive industry. In this regard, it makes sense to consider the balancing trolley in more detail in terms of the calculation of the curves of the realized tire traction. Goal. The goal of this work is to develop a mathematical model of the distribution of normal reactions between the axles of the truck balance in the case of real brake forces between the wheels of the front and rear axle of the truck, which are not linked to each other by an ideal characteristic. Methodology. The proposed method of estimating the distribution of normal reactions on the axles of the truck's balancing trolley during its braking allows to estimate the nature of change of the curves of the tire traction depending on the braking coefficient of the vehicle. Results. The technique allows to take into account: the weight parameters of the vehicle, the geometric parameters of the vehicle, the effectiveness of braking for heavy vehicles. Originally. A new approach is proposed that takes into account the variation of the tilt angle of the balance trolley depending on the load of the heavy vehicle. Practical value. Also, in the paper an example of calculation of the curves of the realized tire traction was made as well as an assessment of the braking performance of a heavy vehicle.