PROBLEM TO BE SOLVED: To provide a seal structure of a rotary machine capable of stably moving seal fins or seal fin opposing portions in the radial direction.SOLUTION: In the seal structure of the rotary machine in which the seal fins or the seal fin opposing portions divided in the circumferential direction are made radially movable according to an operating condition of the rotary machine by utilizing a working fluid pressure and spring force of the rotary machine, a holder into which a working fluid is supplied, and which holds a seal base provided with the seal fins or the seal fin opposing portions, is disposed at a fixing portion side of the rotary machine, an elastic body extended in the circumferential direction, and constituted to increase contact lengths in the circumferential direction, with the holder and the seal base when it is pressed, is disposed between the holder and the seal base, and a holding portion of the elastic body extended in the circumferential direction, is disposed on the holder or the seal base.