A gerotor pump is suitable for oil hydraulics of machine tools, automotive engines, compressors, constructions and other various applications. Especially the pump is an essential machine element of an automotive engine to feed lubricant oil. The subject of this paper is the theoretical analysis of internal lobe pump whose the main components are the rotors: usually the outer one is characterized by lobes with circular shape, while the inner rotor profile is determined as conjugate to the other. For this reason the first topic presented here is the definition of the geometry of the rotors starting from the design parameters. The choice of these parameters is subject to some limitations in odor to limit the pressure angle between the rotors. Now we will consider the design optimization. The first step is the determination of the instantaneous flow rate as a function of the design parameter. This allows us to calculate three performance indexes commonly used far the study of positive displacement pumps: the flow rate irregularity, the specific flow rate, and the specific slipping. These indexes are used to optimize the design of the pump and to obtain the sets of optimum design parameter. Results obtained from the analysis enable the designer and manufacturer of oil pump to be more efficient in this field, and the system could serve as a valuable one for experts and as a dependable training aid for beginners.