A device for supporting a part has a mounting element with a pocket-shaped receptacle and a suction element which supports the part and can be received in the pocket-shaped receptacle or removed from it and directly attached to the surface, so that in both cases the part is supported on the surface, either through the suction element and the mounting element or through the suction element only, and a width of at least a portion of the suction element is smaller than a width of the pocket-shaped receptacle of the mounting element, so that when the portion of the suction element is inserted into the pocket-shaped receptacle of the mounting element, it is compressed and thereby tightly retained in it.