An approach has been developed to research the stability of the wagon flow control systems functioning in railway transport. In general theoretical terms, the approach is based on the construction and comparison of hard and soft mathematical models of the processes under consideration. The mathematical basis of the approach is represented by classical methods in the theory of stability of solutions to autonomous systems of ordinary differential equations. The transport project through which the constructed models are implemented is a control system for empty wagons. The subjects of management are the dispatcher of the operator company and the carrier. The carrier implements feedback in the control system, which in the case of a soft model is expressed in a more complete form than in the case of a hard model. It is shown that with soft modeling, the unperturbed solution of the system of differential equations, which ensures the optimal operating mode of the control system under consideration, is stable in the Lyapunov sense. Moreover, this solution is asymptotically stable. The Maxima system (Free Ware) is used as a modeling software tool. The approach can be used in the research of transportation management issues implemented by other modes of transport.