The computerized design of advanced straight and skew bevel gears produced by precision forging is proposed. Modifications of the tooth surfaces of one of the members of the gear set are proposed in order to localize the bearing contact and predesign a favorable function of transmission errors. The proposed modifications of the tooth surfaces will be computed by using a modified imaginary crown-gear and applied in manufacturing through the use of the proper die geometry. The geometry of the die is obtained for each member of the gear set from their theoretical geometry obtained considering its generation by the corresponding imaginary crown-gear. Two types of surface modification, whole and partial crowning, are investigated in order to get the more effective way of surface modification of skew and straight bevel gears. A favorable function of transmission errors is predesigned to allow low levels of noise and vibration of the gear drive. Numerical examples of design of both skew and straight bevel gear drives are included to illustrate the advantages of the proposed geometry.