This paper describes the development of electromagnetic plasma burn-through model. Full circuit equations describing the currents in solenoid, poloidal field coil, and toroidally conducting passive structure have been integrated into the differential equation system of the plasma energy and particle balances in DYON. This enables consistent calculation of the time-evolving loop voltage at a plasma position only using operation signals in a control room, which are current (or voltage) waveforms in solenoid and poloidal field coils, and prefill gas pressure. The synthetic flux loop data calculated in the modelling agrees well with the measurement in MAST, confirming validity of the loop voltage calculation. The electromagnetic modelling also enables calculation of 2D time-evolving poloidal magnetic flux map, thereby modelling the plasma volume evolution during the plasma break-down and burn-through phase. Only using the control room operation signals used in 34 ohmic start-up discharges with the direct induction scenario in MAST, the electromagnetic plasma burn-through modelling has reproduced the time-evolution of plasma current, electron density and temperature, and plasma volume, showing a reasonable level of agreements with experimental measurement.