This study uses conjugate gear theory to mathematically model the cycloid rotor profile of a Roots pump. After the rotor profile is generated based on the mathematical model of a rotor, a three-dimensional numerical approach can be developed by using the computational fluid dynamics (CFD) solver PumpLinx. The fluid analysis models of cylindrical and screw type Roots pumps are constructed and then a two-lobe rotor is used to illustrate the differences of flow characteristics between cylindrical and screw type Roots pumps. In particular, the models evaluate which of the two pump types achieves a better average outlet flow rate, showing that the cylindrical type pump is better than the screw type but that the outlet flow rate curve of the latter is steadier than that of the former. The findings therefore suggest that the cylindrical type pump should be chosen for efficiency and the screw type pump for steadiness. The results for a simulated pump are similar to those obtained for the real pump, indicating that simulations could serve as a time-saving reference for Roots pump designers.