Abstract: A novel “flexible” algorithm was proposed, for rotor-profile construction and for performance-characteristics evaluation of Roots pump.The self-developed “flexible” algorithm works well for all types of transition/conjugate contours available.Firstly, the upper-limit of shape coefficient was derived to ensure that no interference should exist in the conjugate-contour inside the pitch-circle; next, the “flexible” shape coefficient was described, with the independent variables, including the shape-coefficient, half-peak angle and lobe-number, and in such a way that the peak-point must overlap the start-point of the conjugate contour inside the paired rotor' pitch-circle; and finally, the simplified equations of volume-utilization and flow-pulsation coefficients were derived, respectively.Calculated by assuming a universal type-coefficient of 0.05,the discrepancy of the volume-utilization coefficient was below 0.3%,simply because of a minor impact of the conjugate contour.