Developing rail transport is one of the world's greatest challenges. Rail transport reduces emissions and is the most energy efficient means of transport. An important element of the railways is a hump yard, where rolling stock is formed. The purpose of this article is to describe the mathematical apparatus for calculating the speed of a multiple unit train at a marshalling yard. As a calculation method, the articulated-axis model is used. In this model, the trailer is not seen as a material point, but as several physical bodies. Due to this model, it is possible to simulate multi-carriages moving along heterogeneous profile. It was found that for multi-car trailers the spread of the main co-protection will be lower than for single-car trailers. In addition, as a result of accounting for multi-car trains, the profile requirements are reduced when calculating marshalling yards. The results obtained can be used to design hump yards and automate existing hump yards.