Apparatus and method for minimizing and maintaining substantially constant the effective blade tip clearance between the outer free ends of rotor blades and an adjacent casing shroud of an axial-flow turbine of a gas turbine engine. The casing shroud includes a portion facing the hot gas stream and the outer rotor blade ends and a packing of high heat-resistance, high erosion-resistance ceramic elements secured to the shroud via a metal ring to face the blade tips. A heat insulator is interposed between the packing and the metal ring. A perforated conduit is mounted outside the metal ring for blowing cooling fluid against the metal ring on the side thereof remote from the insulator for equalizing the expansion of the metal ring to that of the turbine wheel. The ceramic packing includes projections facing the outer ends of the blades which are tapered so that they are easily broken off when coming into contact with the blades during running-in of the apparatus.