Since a rigid supporting structure for a gear box GB and a rolling type rack supporting device RSD are employed, an electric power steering apparatus having no response delay and having a high transmission efficiency can be realized. Further, a high steering performance required for a long period and a steering assist force that is increasing recently can be efficiently transmitted to wheels. Further, when the wheels collide with a shoulder of a road to receive a counter input, a torque sensor TS detects a torque and an assist steering force against the counter input is outputted to an output shaft OS Consequently, the torque of the counter input is restrained from being transmitted to a steering shaft SS side. Thus, a kick back and a vibration are advantageously hardly transmitted to a steering wheel SW from the wheels.