The high-frequency impedance of a planar solenoid with a thin magnetic core is theoretically investigated using the magnetostatic Green’s function formalism. It is shown that the electrical behavior of the solenoid depends on how the magnetic field induced by the current-carrying coil is coupled to the different magnetostatic modes of the core. The magnetic response of the core in each mode is determined by an effective susceptibility matrix which depends on exact, but mode-dependent demagnetization factors. Those factors determine the frequency of the magnetostatic excitations of the core, manifested as resonances in the impedance of the solenoid. Using the formalism developed, the effect of the core width and magnetic loss on the impedance of the device is studied.