Abstract: A system for placing items, preferably for parking motor vehicles in a garage, comprises shiftable carrying plates, which carry the items and occupy a plurality of respective carrying plate positions arranged thoughout the available area in rows, which are transverse to each other and preferably at right angles to each other and may be disposed in a plurality of stories, if desired. The carrying plates occupy all but at least one of said carrying plate positions. Shifting means are provided for shifting each carrying plate between each carrying plate position and an adjacent one forwardly and rearwardly in the directions of said rows.