Abstract: A coolable shroud surrounding the tips of the turbine blades of a gas turbine engine is disclosed. The shroud comprises a plurality of arcuate segments which are supported by the turbine case concentrically about the axis of the engine in end to end relationship. Each segment is adapted to receive and distribute cooling air about the walls of the shroud which are exposed to the hot working medium gases flowing through the turbine during operation of the engine. A combination of impingement cooling and transpiration cooling techniques maximize the cooling effectiveness of the air supplied.