In a system for cutting glass sheets into shapes there is at least one cutting site (A, B). In order to align the glass sheet which is to be cut or the glass sheet shape into a defined position, on the edge of the tables I and II there are contact edges (21, 44, 45). In order to move the glass sheets and the glass sheet shapes into contact with the contact edges (21, 44, 45) the tables I, II are aligned sloping down toward the contact edges (21, 44, 45) so that the glass sheets and glass sheet shapes slide on air cushions produced between the glass sheets or glass sheet shapes and the tables (I, II) in contact with the contact edges (21, 44, 45). The glass sheets or glass sheet shapes which adjoin the contact edges (21, 45) are coupled by force-fit to the conveyor belts (20) which are provided in the area of the contact edges (21, 45) and then moved to the cutting site (A, B) which is located following the table (I, II). When there are two cutting sites (A, B) the table (11) can be inclined between the two cutting sites (A, B) such that the intersection point which is used as the reference point (43) between the two contact edges (44, 45) is the lowest point of the table (II).