PROBLEM TO BE SOLVED: To reduce an amount of cooling air used in cooling a turbine shroud for maximizing the overall efficiency of a gas turbine engine.SOLUTION: A composite annular shroud 42 is supported by a support assembly including full 360 degree rings 50, 52, and 54 of integral structure and is disposed within an innermost one of the rings. The shroud is biased against and in sealing engagement 80 with an inner flange 84 of the innermost ring. A three ring assembly includes the inner ring 50 disposed radially inwardly of a middle ring 52 disposed radially inwardly of an outer ring 54 and the shroud 42 at least partially disposed within the inner ring. Three clocking pins 74 extend radially inwardly from the middle ring through a slot 76 in the inner ring into notches 78 in the shroud. A mounting pin 104 is press fitted into a pin hole 106 in the middle ring 52 and extends radially outwardly from the middle ring 52 through a radial hole 107 in the outer ring 54.