The invention relates to a method and a device for evacuating hollow spaces, especially hollow sections (1″, 1′″, 1″″) of plastic windows, wherein an opening (16) is produced in an outer wall (18) of the hollow section (1″, 1′″, 1″″). Air is evacuated from the hollow section (1″, 1′″, 1″″) and the opening (16) is then closed. In order to improve the insulating effect of said method and device, the opening (16) is closed off by a suction tube (8) and a seal (2) is put onto the opening (16) to close the same once the air has been evacuated.