Helicopter structures suffer from excessive vibration originated from many sources including dominant main and tail rotor excitations. Some of these vibration contributors can be identified very easily because of their unique frequency characteristics, such as blade passing frequencies. Additionally, transmission gearboxes are also key sources that show themselves at several gear mesh frequencies. In a gearbox, the transmission error is the phenomena that turn meshing gears into a powerful vibration source at several helicopter zones. Transmission error is the difference in translated rotation between gears due to gears deformation in contact and manufacturing errors. Since, there is a direct correlation between the transmission error and gear induced vibration, reducing the peak to peak transmission error in a gear mesh cycle is a crucial step in gearbox design. In general, the transmission error reduction is done by modifying the tooth profiles in micro scale by using transmission error analytical models. These models are not suitable to reflect the effect of gear web topology and rim thicknesses. So FEA is mandatory to take into consideration the effect of web topology and rim thicknesses on gear pair global stiffness which in turn plays a role in peak to peak transmission error calculation. While reducing the transmission error, other concerns such as tooth root stress and gearbox modal characteristics should also be controlled in order to have a feasible design solution. So design of a gearbox becomes a multi-objective optimization problem with several manufacturing and sizing constraints.