A system for moulding 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 mould member provided with at least one mould cavity, the frame supporting the mould member, mass feed means for feeding the mass to the one or more mould cavities of the mould 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 mould member is removable from the frame. The system has a storage device for storing a plurality of mould members, which may be provided with an identification, has recognition means for recognizing the identification of a mould member, and may have a memory for storing at least one history of a mould member.