A lightweight and low cost gear housing for a steering gear unit is achieved. Together with forming an outward-facing flange shaped convex engagement section 43 around the middle section in the axial direction of a rack shaft 40, a gear housing is constructed that comprises a pinion-side housing 10, a non-pinion-side housing 20, and an intermediate cylindrical section 30. As a result, movement of the rack shaft 40 toward the pinion side and the non-pinion side is restricted by both ends of the pinion-side housing 10. Therefore, portions that require large strength can be limited to the pinion-side housing 10 that is short in the width direction of the vehicle, so by reducing the wall thickness of the intermediate cylindrical section 30, or by making the intermediate cylindrical section 30 using a flexible material, it is possible to make the member lightweight, as well as processing become easier, so it becomes possible to reduce the manufacturing cost.