The article deals with eddy-current (electrodynamic) separators with a traveling magnetic field based on linear inductors. Such separators have high performance and easily fit into finished production lines. They are effective in extracting non-ferrous metals from various types of bulk materials (automobile scrap, mixed industrial and municipal waste, cable and electronic scrap, etc.). Separators are also used for sorting non-ferrous metal scrap in preparation for metallurgical processes. This article focuses on the eddy-current separator, which is based on a conveyor that moves the processed materials, and a three-phase linear inductor located under the conveyor belt. The purpose of the study: improvement of mathematical models and methods for calculating eddy-current separators based on linear induction machines. Results: the proposed method for calculating the physical processes in the separator includes two stages. At the first stage, the calculation of the electromagnetic forces acting on the particles of non-ferrous metals is carried out, according to the methodology developed in Ural Federal University. At the second stage, the trajectories of movement of the separated particles in the working area of the separator are calculated taking into account the combined action of electromagnetic and mechanical forces. At the same time, it is proposed to divide the working separation zone into sections of small sizes. Within such sections, the forces are assumed to be unchanged. The article presents polynomial dependences of electromagnetic forces on the speed of particles and their location above the inductor. Such dependencies allow, in the course of calculations, to correct the forces during the transition from section to section according to the calculated values of the speed and coordinates of the particle. Examples of calculating the trajectories of conductive particles in the working area of an eddy-current separator are presented. The results of the trajectory calculation make it possible to evaluate the results of separation at the stage of plant design.