A machine for making variegated ice cream or ice cream shake, including: a basic structure one or more basic product mixing and freezing units, where each mixing and freezing unit in turn includes a processing cylinder containing the basic product and cooled by a respective refrigerating system and a stirring member mounted inside the processing cylinder and rotating to mix the basic product to prevent it from hardening and sticking to the cooled inside wall of the processing cylinder and to transform the basic product into a basic flavor a closing element for closing the cylinder and provided with at least one outlet duct leading to the processing cylinder at one end and to an outlet mouth at the other end.