Abstract: The invention relates to an apparatus for folding edge sections of molded parts, blanks, or covers provided for them of leather, artificial leather, plastic, or the like, having a sizing plate provided with a cut-out, into which is inserted a pressure plate, the dimensions of the cut-out in the sizing plate corresponding to those of the finished molded part or blank or of a part of it, having a folding plate, on whose side facing the sizing plate, edges are formed for folding over the edge sections of the molded part, blank or cover, and having a base die for accommodating the sizing plate and the pressure plate, the pressure plate inserted into the cut-out of the sizing plate preferably being flexibly supported on the base tool and being vertically movable with respect to the sizing plate and the base die, and the folding plate being retained on a fixing plate, which is vertically movable, for example pneumatically or hydraulically, so as to allow the folding plate to be set down on the sizing plate, as well