A rotary electric machine is provided in which the press-fit load of a stator magnetic pole to a frame is stabilized, thus stabilizing the performance of the rotary electric machine, and that has high anti-corrosiveness and anti-rusty sealing property and is inexpensive. Particularly a rotary electric machine suitable for a motor for motor power steering apparatus is provided. In a rotary electric machine having a stator magnetic pole press-fitted and fixed on an inner circumferential surface of a cylindrical frame made of a steel plate and having a rotor arranged via a gap to an inner circumferential side of the stator magnetic pole, the frame is formed by pressing a surface-treated steel plate having a plating layer of aluminum, magnesium, silicon, and zinc for the remaining part formed on a surface of the steel plate, into a cylindrical shape.