A shroud assembly is provided for a gas turbine engine having 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. The shroud segment has an arcuate, axially extending mounting flange. A shroud hanger includes an arcuate, axially-extending hook. A dimension of one of the shroud segments and the shroud hanger are selected to produce a preselected dimensional relationship therebetween at the hot operating condition.