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This paper presents a mathematical and numerical model developed for coupled time-dependent electromagnetic, temperature and mechanical processes, which occur in polarizable and magnetizable electroconductive solids subjected to an electromagnetic field generated by external currents. The electromagnetic field in the solid and in its surroundings is described by Maxwell's equations. The temperature variation in the solid is governed by the classical heat-transfer equation. To predict the stress-strain state of the solid, a nonisothermal theory for thermoplastic materials is used. The model takes into account the temperature dependence of all material coefficients and the nonlinear dependence of the induction on the strength of both the electrical and the magnetic fields. The problem is solved by a finite-element method and a unified set of single time-step algorithms. As an example, the process of high-temperature induction heating of a finite cylinder is considered.

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