Purpose. At the stage of development of modern information systems for controlling the process of breaking up trains on the humps, the main task is to determine such conditions for cuts' rolling, under which the established safety requirements for breaking up, as well as the requirements for the safety of wagons and cargo in them, are fulfilled. The determination of such rolling modes is undoubtedly a rather complex optimization problem, the solution of which is being addressed by a large number of scientists. In this regard, it can be considered that this problem remains relevant, therefore, the purpose of this research work is to determine such modes of braking of cuts of the train, which ensure their reliable separation when rolling from the top of the hill to the sorting tracks. Methodology. To carry out research on the process of dismantling trains on the hump, the method of simulation was used, and to search for the braking modes of the cuts of the calculation group, the Box complex method was used. Findings. The conditions for separating cuts of the calculated group of the train were investigated, and an iterative procedure was developed to optimize the braking modes of all the cuts of the train, which makes it possible to ensure the maximum value of the minimum interval in the calculated group. In this case, the specified procedure takes into account the intervals between the cuts, both on the arrows and on the retarders of the brake positions of the downhill part of the hill. Originality. It has been established in the work that when determining the modes of braking the cuts of the train, it is necessary to take into account the possible separation of the cuts on all elements of the downhill part of the hill - arrows and retarders. The problem of finding the optimal braking modes for all cuts of the train has been formalized and solved, which, in turn, allow providing reliable conditions for separating adjacent cuts at the turnouts and brake positions of the downhill part of the hill. Practical value. The developed method can be used in the study of the sorting process, as well as in the automation systems for disbanding trains on the hump when determining the braking modes of the cuts.