An apparatus for producing a pasta filata cheese product, such as a Mozzarella-type cheese, in a continuous process without emulsifier or pH regulator additives requires preparing a typical pasta filata-type cheese curd and supplying the curd in cut pieces to one end of a processing chamber (14). The chamber (14) has an agitator (18) which rotates to work, knead, stretch and move the curd through the chamber. At the same time, steam is injected into the curd in the chamber through a plurality of injection nozzles (23) spaced along the length of the chamber (14) to heat and cook the cheese while it is simultaneously mechanically worked. The cooked product exiting from the chamber (14) is molded to a desired shape.