A rear wheel steering apparatus (AU) for a vehicle mounted to a suspension mechanism to steer rear wheels (RL, RR), the rear wheel steering apparatus (AU) comprising: a housing connected via a first connection member and a second connection member to the suspension mechanism that supports the rear wheels (RL, RR) of a vehicle; an electric motor accommodated within a cylindrical body that constitute a portion of the housing ; a deceleration mechanism accommodated within the cylindrical body to decrease an output of the electric motor ; a linear motion mechanism including a nut member connected to the deceleration mechanism to rotate and a rod meshed with the deceleration mechanism and connected to the second connection member , the linear motion mechanism converting a rotary motion of the nut member to a linear motion of the rod ; a connection cover including the first connection member and closing an opening portion of the cylindrical body at a side facing the deceleration mechanism ; and a rotor constituting a portion of the electric motor and including a hollow rotation shaft supported by the cylindrical body to be rotatable relative to the cylindrical body , characterized in that the rotor constituting a back yoke fitted to an outer peripheral surface of the hollow rotation shaft and integrally rotating with the hollow rotation shaft , the back yoke including a cylindrical form, and a plurality of permanent magnets arranged at the back yoke at even intervals in a circumferential direction of the back yoke ; the back yoke including a plurality of projecting portions each of which includes an inner peripheral surface formed in an arc shape in a cross section, the inner peripheral surface projecting towards an axial center of the hollow rotation shaft and extending in an axial direction of the hollow rotation shaft , an inner radius (R1) of the inner peripheral surface formed in the arc shape in the cross section being specified to be greater than an outer radius (R0) of the outer peripheral surface of the hollow rotation shaft and a distance (D) between a circumferential center of the inner peripheral surface formed in the arc shape in the cross section and the axial center of the hollow rotation shaft being specified to be equal to the outer radius (R0) of the outer peripheral surface of the hollow rotation shaft , the back yoke being press-fitted to the outer peripheral surface of the hollow rotation shaft via the plurality of projecting portions . a housing connected via a first connection member and a second connection member to the suspension mechanism that supports the rear wheels (RL, RR) of a vehicle; an electric motor accommodated within a cylindrical body that constitute a portion of the housing ; a deceleration mechanism accommodated within the cylindrical body to decrease an output of the electric motor ; a linear motion mechanism including a nut member connected to the deceleration mechanism to rotate and a rod meshed with the deceleration mechanism and connected to the second connection member , the linear motion mechanism converting a rotary motion of the nut member to a linear motion of the rod ; a connection cover including the first connection member and closing an opening portion of the cylindrical body at a side facing the deceleration mechanism ; and a rotor constituting a portion of the electric motor and including a hollow rotation shaft supported by the cylindrical body to be rotatable relative to the cylindrical body , <EOS>