A shroud sealing arrangement for a gas turbine engine, which comprises a static shroud assembly mounted to an engine case and having a platform surrounding a rotatable airfoil array. The platform has an inner side and an outer side and extends from a leading edge to a trailing edge. A shroud support structure mounts the shroud platform to the case. A circumferential groove is defined on the outer side of the shroud platform proximal to one of the leading edge and the trailing edge. A sealing ring is set in the groove and adapted to seal cooling air from escaping directly to the gas path.