An electric power steering apparatus including: a ball screw shaft that is integral with a rack shaft provided so as to be movable relative to a housing in a vehicle-width direction; a ball screw nut rotatably mounted on the ball screw shaft, the ball screw nut being fitted at a portion of an outer periphery on one side in an axial direction, to the housing via a bearing such that the ball screw nut is rotatable relative to the housing and immovable in the axial direction relative to the housing; a driven toothed-pulley fixedly fitted onto a portion of the outer periphery of the ball screw nut on the other side in the axial direction, the driven toothed-pulley being configured to rotate together with the ball screw nut in an integrated manner; an electric motor mounted on the housing, the electric motor being configured to generate rotary torque; a driving toothed-pulley configured to be transmitted rotary torque generated by the electric motor, the driving toothed-pulley being located at the same position in the axial direction as the driven toothed-pulley; and a toothed belt looped over the driving toothed-pulley and the driven toothed-pulley, configured to transmit the rotary torque generated by the electric motor to the ball screw nut, the electric power steering apparatus being configured to provide steering assistance by using an axial driving force that is applied to the rack shaft when the rotary torque generated by the electric motor is transmitted to the ball screw nut, and the electric power steering apparatus being configured such that an amount of axial travel of the rack shaft is limited when a rack end provided at an end of the rack shaft and the housing come into contact with each other in the axial direction, the electric power steering apparatus further comprising a tilt allowing portion configured to cause the ball screw nut to tilt relative to the ball screw shaft such that a distance between a center of rotation of the driven toothed-pulley and a center of rotation of the driving toothed-pulley increases when the rack end and the housing come into contact with each other in the axial direction, the electric power steering apparatus being characterized in that in a case where the driven toothed-pulley, the driving toothed-pulley, and the toothed belt are disposed between the bearing and the rack end, the tilt allowing portion is included in the housing; and in the tilt allowing portion, axial stiffness of a housing first stopper portion (62a1) that restricts an axial displacement of the bearing on the driving toothed-pulley side of the bearing is set lower than axial stiffness of a housing second stopper portion (62a2) that restricts the axial displacement of the bearing on the driven toothed-pulley side of the bearing. a ball screw shaft that is integral with a rack shaft provided so as to be movable relative to a housing in a vehicle-width direction; a ball screw nut rotatably mounted on the ball screw shaft, the ball screw nut being fitted at a portion of an outer periphery on one side in an axial direction, to the housing via a bearing such that the ball screw nut is rotatable relative to the housing and immovable in the axial direction relative to the housing; a driven toothed-pulley fixedly fitted onto a portion of the outer periphery of the ball screw nut on the other side in the axial direction, the driven toothed-pulley being configured to rotate together with the ball screw nut in an integrated manner; an electric motor mounted on the housing, the electric motor being configured to generate rotary torque; a driving toothed-pulley configured to be transmitted rotary torque generated by the electric motor, the driving toothed-pulley being located at the same position in the axial direction as the driven toothed-pulley; and a toothed belt looped over the driving toothed-pulley and the driven toothed-pulley, configured to transmit the rotary torque generated by the electric motor to the ball screw nut, the electric power steering apparatus being configured to provide steering assistance by using an axial driving force that is applied to the rack shaft when the rotary torque generated by the electric motor is transmitted to the ball screw nut, and the electric power steering apparatus being configured such that an amount of axial travel of the rack shaft is limited when a rack end provided at an end of the rack shaft and the housing come into contact with each other in the axial direction, the electric power steering apparatus further comprising a tilt allowing portion configured to cause the ball screw nut to tilt relative to the ball screw shaft such that a distance between a center of rotation of the driven toothed-pulley and a center of rotation of the driving toothed-pulley increases when the rack end and the housing come into contact with each other in the axial direction, the electric power steering apparatus being characterized in that in a case where the driven toothed-pulley, the driving toothed-pulley, and the toothed belt are disposed between the bearing and the rack end, the tilt allowing portion is included in the housing; and in the tilt allowing portion, axial stiffness of a housing first stopper portion (62a1) that restricts an axial displacement of the bearing on the driving toothed-pulley side of the bearing is set lower than axial stiffness of a housing second stopper portion (62a2) that restricts the axial displacement of the bearing on the driven toothed-pulley side of the bearing.