Abstract The article discusses possible options for a low-temperature induction heating system (LTIHS) of flat metal products in a traveling electromagnetic field. The problem of calculating eddy currents, active and reactive powers induced in a heated flat object, as well as electromagnetic forces acting on the object moving it in a given direction, is posed and solved. A mathematical model has been developed that takes into account the dependence of the influence on the main parameters of the electromagnetic field of the following factors: geometric dimensions of the air gap between the poles of the magnetic circuit and the heated flat body; the longitudinal edge effect caused by the open circuit of the magnetic circuit of the inductor, as well as the transverse edge effect associated with the appearance of the longitudinal components of eddy currents in a heated flat object. The solution of particular problems of LTIHS in one- and two-dimensional formulation allows them to be simplified and to perform calculations for various design variants of induction heating devices with a traveling electromagnetic field, using a one-dimensional model that explicitly takes into account the features of electromagnetic processes in the systems under study.