A retarder, as a supplementary brake system that is not friction-based, is frequently used in heavy-duty vehicles generally to slow the vehicles down on inclines. The electric retarder mainly used in a heavy-duty bus is generally placed between the transmission and the axle. The rotor inside the retarder system is attached to the axle. The operation of the retarder within a driven vehicle generates reverse torque due to coast driving force on hypoid gears in the differential gear system. By the reverse torque, scoring or scuffing on the hypoid gear teeth may directly occur. The scoring may be generated due to excessive contact stresses on the tooth surface. In this study, tooth contact stresses and contact patterns were analysed in order to investigate on the tooth scoring phenomenon using a finite element analysis program T900 in which the Hertzian contact stress formula was taken. Backlash, wear and surface finish were considered in the finite element simulation on the scoring.