A machine (1) for making liquid or semi-liquid food products, comprises: a processing chamber (2) for processing a basic mixture and provided with a stirrer (3) and with thermal treatment means (4) for the basic mixture, operating in conjunction with one another to convert the basic mixture into a liquid or semi-liquid product; an electronic drive and control unit (5); a dispensing device (6) having a dispensing nozzle (7) connected to the processing chamber (2) to deliver the liquid or semi-liquid product; a support (8) having a seat (9) for housing a receiving container (10); movement means (11) for vertically moving the support (8) between a vertical position (P1) away from the dispensing nozzle (7) and a vertical position (P2) close to the nozzle (7); means (12) for rotating the housing seat (9) and configured to allow the housing seat (9) to be rotated about a vertical axis (Y); the electronic drive and control unit (5) is operatively connected to the movement means (11) and to the means (12) for vertically rotating the housing seat (9) in order to drive them according to a predetermined law of motion. [Figure 1]