A torsion beam which is used in a suspension system of an automobile which is provided with a pair of arm members which extend in a front-rear direction of the automobile and are designed to be connected to a chassis of the automobile so as to be able to swing and to have wheels attached rotably to them is disclosed. The torsion beam is formed with a recess which extends in the longitudinal direction whereby that torsion beam has first and second leg parts in a plane vertical to the longitudinal direction and exhibits a substantially V-shaped or substantially U-shaped cross-sectional shape. The torsion beam is provided with connection parts which are provided at the two ends of that torsion beam and are connected to the arm members, a fixed shape part which is provided at a center part in the longitudinal direction of that torsion beam, and asymmetric shape parts which are provided between that fixed shape part and the connection parts. At the asymmetric shape parts, the depth of the recess becomes gradually deeper from the connection parts toward the fixed shape part and the first leg part has a larger width dimension than the width dimension of the second leg part.