The paper presents a method for calculating normal reactions of the road bearing surface along the axles of a multi-axle wheeled vehicle, upon which it is possible to construct the adhesion utilization curves for all vehicle axles, considering that both independent axles and axles combined in balancing trolleys are present in the vehicle suspension. The main idea of this method is developing a universal mathematical model for determining the horizontal coordinate of the center of elasticity (center of rotation) of a multi-axle vehicle body with reference to which the normal reactions along the axles of the vehicle during its braking are determined. In addition, with a known distribution of braking forces, the adhesion utilization curves are plotted. In the overview part, an analysis is given that showed that there is no single methodology or recommendations today regarding determination of normal road reactions on the axles of a multi-axle wheeled vehicle. The developed methodology can be applied in engineering calculations when checking multi-axle wheeled vehicles for compliance with international requirements for brake systems (Appendix 10 to UN / ECE Regulation No. 13). The universality of the proposed methodology allows recommendation for its implementation in the given Rules No. 13. The calculations of the adhesion utilization curves made on the example of a 4-axle vehicle showed that consideration of the design features of a multi-axle wheeled vehicle suspension significantly affects the nature of the geometry of the adhesion utilization curves within the permissible limits specified by UN / ECE Regulation No. 13 (Appendix 10).