In the design of gear pairs, the designer has to make design trade-off between the geometrical volume and the meshing vibration. It is generally known from experience that the two objectives show conflicting tendency. In this paper, the authors demonstrate the analysis results of the relation between the geometrical volume and the vibration of a gear pair, and propose a design method for cylindrical gear pairs to balance the conflicting objectives by using a goal programming formulation. The design method reduces both the geometrical volume and the meshing vibration of cylindrical gear pairs while satisfying strength and geometric constraints. The validity of the method will be shown through the design results of the four cases of design speeds and the redesign of a helical gear pair currently being used in elevator reduction drive.