A motor for an electric power steering apparatus can ensure an appropriate preload to an outer race of a rolling element bearing by adjusting the thickness of a spacer without replacement of a wave washer for a change in an axial dimension between a bottom surface of a bearing box and the bearing. The motor includes a rotor, a casing that receives the rotor and has the bearing box in which the bearing rotatably supporting a shaft of the rotor is received, an annular wave washer that is arranged between the bottom surface of the bearing box and the bearing, and applies a preload to the outer race of the bearing, and an annular spacer that is arranged between the bottom surface of the bearing box and the bearing so as to be in abutment with the wave washer for adjusting the preload applied to the outer race.