A turbine shroud (30) of a gas turbine engine comprises a plurality of arcuate shroud segments (31) combined into an annular configuration, each shroud segment including a main body (32) defining an inner circumferential surface opposing the tips of the turbine rotor blades (11a) at a small clearance and an engagement feature including an axial wall (33a, 34a) having a prescribed circumferential length and a prescribed axial length, the turbine casing including an axial slot (51, 52) extending coaxially around the center line of the engine and configured to receive the axially extending wall of each shroud segment. A clearance defined between each circumferential end part (E) of the axial wall and an opposing inner circumferential surface of the turbine casing is greater than that defined between a circumferentially middle part (M) of the axial wall and an opposing inner circumferential surface of the turbine casing under a cool condition of the engine. A radial temperature gradient that develops in each shroud segment when the engine is warmed causes a deformation of the shroud segment such that the clearance can be made substantially uniform over the entire circumference of the shroud segment and the cooling air leakage can be minimized while minimizing thermal stress that may be caused by the thermal expansion of the shroud segment.