Along with the improvement of existing switch machines by replacing unreliable elements, the company produces the world work on the creation of new types. The general concept of the new turnouts for both conventional and high-speed movement, is to ensure maximum reliability and safety, as well as to reduce the time spent on laying and maintenance turnout by avoiding the pre-installation on the secondary site, reduce energy consumption, function, capacity drive. Modern turnouts are equipped with modified and optimized drive system. Therefore, in this paper we consider a mathematical model of the actuator on the basis of a linear motor for the purpose of its further use as a basic tool in the study of modes in the turnouts. It is possible to obtain the dynamic characteristics of the machine. For simulations as input parameters taken linear motor proposed in the previous works. The mathematical description of linear electromechanical transducer is derived from the Lagrange equations.