To provide a tolerance ring for torque transmission device, capable of preventing eccentricity which occurs between both of two axial members.

In a torque transmission device T, the both axial members S1 and S2 which are in a double axial form have a tolerance ring 10 fitted therebetween. When an input torque is smaller than a set torque, the tolerance ring 10 rotates the both axial members S1 and S2 integrally, whereas when the input torque is greater than the set torque, causes slipping between the both axial members S1 and S2 to permit relative rotation of the both axial members S1 and S2, so as to function as a torque limiter. In the tolerance ring 10, a ring body 11 having a cylindrical shape with a joint potion formed between both circumferential end edges and having spring properties has a large number of convexities 13 formed at predetermined intervals in the circumferential direction. The rigidity of a pair of convexities 13 provided neighboring the joint portion of the ring body 11 is equivalent to the rigidity of the convexities 13 disposed in the diametrical half of the same on the side opposite to the joint portion 12.