Abstract: We addressed the problems of circumferential leakage and trapped-gas of Roots vacuum pump. The total solutions included: first, two new types of arc-rotor were developed and mathematically modeled; next, their profiles and parametric equations were analytically derived; and finally, their geometries were parameterized and optimized. The operation of exemplified Roots pump with the two novel types of arc-rotor was theoretically analyzed.The calculated results show that the novel arc-rotors all significantly outperform the conventional one, because of smaller circumferential leakage, complete removal of trapped-gas, easier machining and lower fabrication cost. We suggest that the newly-developed arc-rotors may be of much technological interest in fabrication of Roots vacuum pump.