A machine (1) for making and dispensing liquid or semi-liquid products comprises, in combination: - a plane element (9) with an opening (9A) made in it; - at least one container (2) adapted to contain a basic mixture provided with an opening (5) and inserted in the opening (9A) of the plane element (9); - a stirrer (3) and a refrigeration system (4), operatively associated with the container (2) respectively for mixing the basic mixture and for cooling the basic mixture in such a way as to convert it into finished product; - a flange (10) which can be coupled to the plane element (9); - means (30) for coupling the flange (10) to the plane element (9); - a lid (7) movably connected to the flange (10) to close the opening (5) of the container (2) in use.