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Purpose – Nowadays, various software is available for simulating physical processes in induction heating. The software is often limited in its ability to simulate the billet movement, sometimes assuming uniform distribution of voltages on the inductor winding, uniformity of the physical properties of the billet, etc. The mathematical model of moving cylindrical ferromagnetic billets described in this paper takes into account the billet's movement, the billet phase heterogeneity and the nonuniformity of the supply voltage distribution in the inductor turns. The paper aims to discuss these issues. Design/methodology/approach – The research methodology is based on FEM analysis of the coupled problem, including the electromagnetic and thermal boundary problem with additional algebraic equations, using Comsol 3.5a software. Findings – The electromagnetic and temperature field in the billet and the voltage distribution on the winding turns have been calculated. The phase distribution in the billet has been predicted. Significant interaction of the nonuniformity of the supply voltage distribution, the billet's movement, the billet phase heterogeneity and side effect on the ends of the inductor have been shown. Practical implications – The results received can be used for designing the induction heating unit for moving cylindrical billets made from ferromagnetic material and improving their characteristics. Originality/value – Investigation of moving cylindrical ferromagnetic billets induction heating can be done by numerical solving the coupled problem including the electromagnetic and thermal boundary problem with additional algebraic equations for the supply voltage distribution. [ABSTRACT FROM AUTHOR]