This paper presents a newly developed analytical model with application in profiling the hob mill for generating a pump rotor having four circular lobes with rectilinear directrix. The analytical model of rotor surface is deducted at first. The generating rack-tool is secondly determined and then, the peripheral surface of the hob mill results as envelop of surfaces family generated by the successive positions of generating rack-tool. The profiling solution lies on the fundamental theorems concerning the reciprocal enwrapped surfaces. A calculus algorithm and a numerical model developed in MatLab are proposed. The characteristic curve of hob mill tooth surface is found out in the case of a given rotor profile. Index Terms-Quadrilobed rotor, analytical model, hob mill profiling, intermediary surface method.