A field-theoretical approach is used to analyze the subject of magnetic induction heating of thin circular plates by planar coils. Closed-form solutions for the electric and magnetic fields are found to the basic field problem of a single circular loop carrying current at a frequency ω in the presence of a plate characterized by a permeability μ and conductivity σ. By using these fields, expressions are derived for the complex Poynting vector at the surface of the plate, and for the induced EMF in the coil. The theory is extended to include multiturn coils and a field-dependent permeability, and a specific multiturn coil and plate combination is chosen as an example. The complex amplitude of the magnetic field and the Poynting vector are calculated along the surface of the plate using iterative methods to assure self-consistency with the field dependent permeability of the plate. By using Fourier transform techniques, the transient coil current and coil voltage waveforms are calculated under the experimental conditions used to take data on the sample coil and plate. The absorbed power is calculated from these waveforms and is found to be within 10 percent of the measured power absorption for all levels of operation from 50 to 2000 W. The calculated coil current waveform is compared with the measured waveform and is found to be in very good agreement in both shape and period.