A shroud assembly is provided for a gas turbine engine that has a temperature at a hot operating condition substantially greater than at a cold assembly condition thereof. The shroud assembly includes: at least one arcuate shroud segment adapted to surround a row of rotating turbine blades which has an arcuate, axially extending mounting flange; a shroud hanger having an arcuate, axially-extending hook disposed in mating relationship to the mounting flange; and an arcuate C-clip having inner and outer arms overlapping the hook and the mounting flange. The curvatures of the mounting flange and the inner arm of the C-clip are selected so as to define a matched interface therebetween. Their curvatures are substantially greater that the curvature of the hook.