PURPOSE: To eliminate the excessive play of a handle and prevent the occurrence of reduction of a steering auxiliary force by inserting a piston in an inner cylinder and radially and elastically displaceably supporting the inner cylinder to a housing.

CONSTITUTION: An inner cylinder 40 is radially displaced and a ball nut 7 is radially displaceable. When radial pressurization is applied on the ball nut 7, the ball nut 7 is radially displaced, the ball nut 7 and a ball screw 2 are pressed against each other through a ball 6 and a relative clearance between the ball screw 2 and the ball nut 7 is removed. Since a piston 8 is pressed against the inner surface of the inner cylinder 40 and the inner cylinder 40 is radially elastically displaced, friction between the piston 8 and the inner cylinder 40 is reduced. This constitution prevents wear of the inner surface of the inner cylinder 40 and prevents the occurrence of leakage of oil between a pair of oil chambers 46 and 47.