A structure for fastening a stiffening bar includes a floor panel covering a bottom side of a vehicle body. A sub-frame is mounted on the floor panel and extends in a width direction of the vehicle body. A pair of center side members are mounted to the sub-frame and extend longitudinally at both sides of the bottom side of the vehicle body. A pair of rear side members extend longitudinally below the pair of center side members. The stiffening bar is mounted to the pair of rear side members so that a bottom side of the stiffening bar is higher than bottom sides of the pair of rear side members.