An electric power steering apparatus having a motor for producing assist torque according to the steering torque, and a rack and pinion mechanism for transferring torque assistance to the rack shaft. The pinion and rack of the rack and pinion mechanism are both helical gears, and transfer high torque to the rack shaft. The helical gears have a curved arc tooth profile. The teeth of a curved arc tooth profile gear set mesh with contact between convex and concave surfaces. The contact area is therefore increased and contact pressure is decreased compared with involute teeth. Surface fatigue strength, bending strength, and bending fatigue strength are thus greater compared with involute teeth. The combined steering torque and assist torque is efficiently transferred to the rack shaft, and durability is sufficient to withstand torque loads from motor inertia.