Abstract: We theoretically addressed the general criteria for and calculation method of the maximum shape-factor of the Roots pump rotors,whose shape-profiles are different.First,the principal shape-profile sections of a specific rotor type were defined and called the “valley/peak” sections for short; second,the conjugate Maximum-point of shape-factor at the peak-section was reversely derived in terms of the extremized point of the valley-section,at which the curvature-radius was zero,and by solving Euler-Savery equation for conjugate geometry,consequently,the two unknown coefficients in the peak-section definition could be calculated; third,the method for calculating the maximum shape-factor was developed,and finally,two general criteria were developed.The maximum shape-factor of the circular-arc rotor was calculated precisely and rapidly with the newly-developed general criteria and calculation method.The calculated results were in good agreement with those reported in literature.