A semianalytical model is derived for the description of the three-dimensional magnetic fields, generated by an array of air-cored rectangular coils above a ferromagnetic plate with cavities, or bounded slots, in the xy-plane. The magnetic fields are described with a double Fourier series and are obtained by solving the Maxwell equations using a combination of the magnetic vector and scalar potentials. Mode-matching of the double Fourier series is applied to obtain the description of the magnetic fields inside the cavities. Therefore, the mode-matching technique is extended for two dimensions. The semianalytical model is compared with three-dimensional finite element analysis and a good agreement has been found.