A internal lobe pump is suitable for oil hydraulics of machine tools, automotive engines, compressors, constructions and other various applications. In particular, 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. The topic of this paper is the design of a new rotor, which is based on specific performance as different types depending on the shape of the lobe of the outer rotor. First, the design of internal lobe pumps with circular, elliptical, and their combined lobe profiles is considered. The latter is a new type of lobe profile with special shape whose curvature follows a definite function. Then we introduce the performance indexes used for the comparison. Some of these indexes, such as flow rate and flow rate irregularity, are commonly used for the comparison, while specific slipping is particularly suitable in this case. It is possible to notice that the circular and elliptical type is comparable to the circular one or the elliptical one in terms of flow rate irregularity, but has improved performance in terms of specific slipping. Results obtained from the analysis enable the designer and manufacturer of oil pump to be more efficient in this field.