A shroud attaching structure of a gas turbine includes: a support provided around an axis of the gas turbine and inside a casing of the gas turbine in a radial direction; and a shroud assembly attached to the support so as to cover an inner peripheral surface of the support, the shroud assembly being formed by laminating a large number of plate-shaped shroud elements containing a ceramic matrix composite. The shroud elements are lined up in a circumferential direction of the support. The adjacent shroud elements are arranged so as to be slidable on each other.