Abstract: A steering shaft for motor vehicles which comprises an inner and an outer shaft part. Each shaft part has a polygonal cross section. The shaft parts engage one another in telescoping fashion and are positively connected to one another by barrel-shaped rolls that are effective as rolling elements for the transmission of a torque. The running paths of the rolls are fashioned between vertices on the outer sides of the inner shaft part and the inner sides of the outer shaft part and are designed so that the running paths are fashioned as troughs of a concavity approximating to the convexity of the rolls.