A turbine shroud apparatus for a gas turbine engine having a centerline axis includes: a shroud segment having: an arcuate body extending axially between forward and aft ends and laterally between opposed end faces, wherein each of the end faces includes seal slots formed therein; and an arcuate stationary seal member mounted to the body; a turbine vane disposed axially aft of the shroud segment; and a casing surrounding the shroud segment and the turbine vane; wherein the turbine vane is mounted to the case so as to bear against the stationary seal member, compressing it and forcing the shroud segment radially outward against the casing.