To reduce vibration in the bending direction while restraining mass from increasing with regard to a torque transmission shaft including a structure having a hollow inner shaft coaxially inserted in a hollow outer shaft from one of its ends and uniting the inner circumferential surface of the outer shaft with the outer circumferential surface of the inner shaft through a rubber elastic body.

A first supporting member 6 is fixed to the inner side near the end part 3A of an outer shaft 3 and second supporting member 7 is fixed to the inside near the end part 4A of an inner shaft 4. A long and narrow steel made bar shape member 8 is arranged along the center axis of the inner shaft 4 and both ends of the bar shape member 8 supports the outer shaft 3 or the inner shaft 4 by the first supporting member 6 or the second supporting member 7. Natural frequency of the bar shape member 8 in the bending direction is adjusted so that it may coincide or almost coincide with the natural frequency of mass/spring bending direction vibration on which the outer shaft 3 and the inner shaft 4 actuate as mass and an elastic body 5 actuates as a spring.