When filling the inner space (14) of an insulating glass unit (4) with a filler gas, a pressure is exerted during filling on the outer surfaces of the glass panes (12, 13) of the insulating glass unit (4) to be filled. For this purpose, an apparatus is suggested with a device (5) for feeding filler gas and with a device (6), by which air and/or gas can be removed from the inner space (14) of the insulating glass unit, wherein two pressure plates (1, 2) are provided which can be placed, during the filling step, with a preselectable pressure against the outer surfaces of the glass panes (12, 13) of the insulating glass unit (4).