onto the inflatable body 1 with the load bearing framework 5 extended in such a case in the first instance the flaps 15 of the button strip clamp 13 and the correspondingly configured flaps 10 of the top part 4 are opened the button strip or the buttonhole strip and the collar tips are positioned beneath the flaps 15 and 10 respectively and are fixed by virtue of the flaps 15 and 10 being closed the shirt collar for pressing purposes is tensioned in the circumferential direction by actuation of the collar tensioning and collar clamping device in the top part 4 the fan 6 is then set in operation together with the heating device 7 whereupon heated air is directed into the supporting body 2 from the supporting bodies 2 the air flows through the air permeable enclosures of the same into the inflatable body 1 inflates the latter and then flows through the likewise air permeable enclosure of the latter to the shirt 19 that has been fitted thereon and is pressed by the action of tensioning and heat in the stationary state the pressure prevailing in the supporting bodies 2 is higher than that in the inflatable body 1 for example a level of 6 mbar in the supporting bodies 2.