In the modern, highly developed auto industry, one of the goals is to design components that generate as little noise and vibration as possible, so that the vehicle would be more comfortable for the driver as well as the passengers. One of the biggest sources of vehicle noise is the gearbox. The usual approach is to intervene on the very source of the noise, the gears, to get the effect of reducing the overall noise. The main goal of this master's thesis is reducing the gearbox generated noise by the means of topology optimization of the gearbox housing geometry. For the purposes of testing the optimization method, design of two-stage gearbox for electric drive applications was carried out. The KISSsys software package was used for designing of the gearbox. Three housing variants have been designed. Static topology optimization was conducted on two variants, to satisfy strength and rigidity requirements with minimal use of material. Topological optimization of NVH (Noise, Vibrations & Harshness) signature was performed on the third variant of the housing. To do this, an MBD (Multi Body Dynamics) gearbox model was developed in AVL EXCITE Power Unit software, with the support of AVL-AST d.o.o. Using the software listed, structural noise of the housing was analyzed. Three modes that have the greatest contribution on the vibrations causing the structure-borne noise of the housing were found and their eigenfrequencies were maximized by the topology optimization. That way the structure-borne noise of the housing was reduced. At the end of the thesis, a conclusion was made on the successfulness of the optimization method and the proposals for further improvement and research were presented.