In the case when a multi-link vehicle consists of 3 links or more, the study of their movement is significantly complicated, since the number of factors that influence the nature of the movement of the constituent links of the road train significantly increases. During the movement of a multi-link vehicle the force interaction between its adjacent links significantly affects the entire road train, which can lead to significant deviations of its links from the movement direction set by the tractor truck. Road trains are a type of transport with increased danger, therefore, when designing and researching multi-link vehicles, it is necessary to conduct detailed theoretical and numerous experimental studies of the dynamics of their movement, which will become the basis for predicting their behavior in real conditions. Proceeding from the above, the layout scheme of a road train with 3-axle tractor, 2-axle trolley and 3-axle semi-trailer as universal and promising (developed by the companies “Scania” and “Krone”) was chosen to study its movement and develop a mathematical model of movement. This model will allow us to theoretically predict and determine the influence of our layout scheme and driving modes of 3-link road train on its operational properties. At first time the subject of mathematical modeling became the three-link road truck train with a two-axle trolley and a coupling point located outside the tractor base. This configuration was not the object of in-depth analysis in previous works. This study is comprehensive in nature and demonstrates a number of aspects that distinguish the proposed approach against the background of existing scientific developments in the field of transport system dynamics.