We present both a mathematical model and a numerical method for simulating induction heating processes. The geometry of the conductors is cylindrical and the magnetic field is assumed to be parallel to the invariance axis. The model equations have current tension as prescribed data rather than current intensity. In Particular, the formulation of the electromagnetic problem uses the magnetic field as the unknown function. The numerical method takes into account the time periodicity of the prescribed tension and deals with the two different time scales of electromagnetic and thermal phenomena.