A suspension apparatus for rear wheels of a motor vehicle, including a pair of trailing arms and a torsion beam of substantially U-shaped cross section. In the apparatus, an opening portion of the torsion beam is oriented forwardly or backwardly in a longitudinal direction of a body of the motor vehicle such that a length of a lower horizontal portion of the torsion beam, measured in the longitudinal direction of the body is made larger than that of an upper horizontal portion of the torsion beam.