A positive displacement pump has a casing with a central body and two closing lids, the central body being provided with two cylindrical communicating chambers, one suction pipe and one discharge pipe, and two rotors revolvingly mounted in the chambers of the central body and supported by shafts revolvingly mounted in the closing lids. The two rotors include a male rotor having only protuberances, not cavities, and a female rotor having only cavities, not teeth or protuberances.