Abstract <p>This article is devoted to new approaches to modeling pneumatic processes occurring in the brake system of a train. Various methods are used to model pneumatic processes in various elements of the brake system. Thus, the Navier–Stokes equation is commonly used to model changes in the pressure in the brake line. At the same time, the models of non-stationary processes occurring in the brake line do not take into account the influence of processes in the main reservoir. Indicator diagrams or thermodynamic equations are usually used to model the operation of the air distributor. This approach has insufficient accuracy when compared with experimental studies. To date, the mathematical models used to calculate pneumatic systems have an error of 12–15%. More detailed mathematical models are highly complex and the calculation time of gas-dynamic processes is 100 times slower than the simulated physical processes. The new mathematical models of pneumatic processes proposed in this study are based on the energy approach, similarity theory and motion theory. The maximum value of the relative error when using such approaches reaches 0.7% and appears only at low pressure values, at which its effect on the operation of pneumatic brake systems is insignificant. In addition to sufficient accuracy of the results, this approach does not require complex calculations and allows you to calculate processes in a time hundreds of times faster than their occurrence.</p>