To increase volume displacement is always concerning in designing external gear pumps (EGPs). Therefore, an approach of optimization analysis intending to enhance their displacement capability is proposed in this study. Through that, design parameters of the spur gears in the pumps are systematically resulted to achieve their optimal volume displacements. Parametrically, a CAD model to visualize the designed gear of the optimal design is also created. Firstly, the study derives tooth profile equations by using the coordinate transformation and equation of meshing for gears on a rack cutter profile. Then, an analytic formula represented the enveloping area by an involute curve is derived. Next, volumes of output and trapped backflow of the EGP are achieved. Therefore the net output volume can be calculated accurately and efficiently. After that, the optimization analysis to maximize the volume displacement is performed. Through that, optimal design parameters for the pumps are achieved under assigned constraints for considerations of design and manufacturing. Additionally, influences of module, pressure angle, and addendum correction factor for the gears in the pumps on their displacement capability are also investigated. Additionally, flowrate fluctuation characteristics under different pressure angles of gears are finally discussed.