A system for molding three-dimensional products from a mass of one or more food starting materials which are suitable for consumption, in particular human consumption, has a production device having a frame, a mold member provided with at least one mold cavity, the frame supporting the mold member, mass feed means for feeding the mass to the one or more mold cavities of the mold member. The system also has at least one cleaning device for cleaning one or more parts of the production device which come into contact with the mass. The mold member is removable from the frame. The system has a storage device for storing a plurality of mold members, which may be provided with an identification, has recognition means for recognizing the identification of a mold member, and may have a memory for storing at least one history of a mold member.