New geometry of face worm gear drives with conical and cylindrical worms is proposed. The generation of the face worm-gear is based on application of a tilted head-cutter (grinding tool) instead of application of a hob applied at present. The generation of a conjugated worm is based on application of a tilted head-cutter (grinding tool) as well. The bearing contact of the gear drive is localized and is oriented longitudinally. A predesigned parabolic function of transmission errors for reduction of noise and vibration is provided. The stress analysis of the gear drive is performed using a three-dimensional finite element analysis. The contacting model is automatically generated. The developed theory is illustrated with numerical examples.