For the evaluation of the load carrying capacity of gear wheels, the knowledge of the true stress at the tooth root fillet is of extreme importance. The aim of the diploma thesis is to verify the stress predictions resulting from numerical simulation with the DIN 3990 standard. An adequate 2D shape of the involute gear tooth is one of the basic requirements for generating a finite element model. Although the stress distribution in the tooth root fillet is of main interest for an assessment of the load carrying capacity the tooth flank also has to be well defined. Otherwise contact problems will appear, the conjugated tooth action may be influenced and the tooth flanks may lift off at the contact point when two gears are in mesh together. Furthermore an adequate refinement of the FE mesh and selection of the proper element type helps to get reliable simulation results. To meet the requirements of transmitting constantly increasing power in modern drives it is necessary to optimise the transmission while keeping reducing the total weight. Keywords like topology optimisation and shot peening are well established, and an improved shape of the tooth root fillet seems to be best for keeping the tangential stress along the fillet as smooth as possible. A finite element study about different root modifications gives a short overview how the stress distribution in the fillet can be influenced.