A method of machining a turbine shroud segment including inserting an annular flange of a grinding wheel through a first gap defined between the shroud retention elements and into a second gap defined between the shroud platform and an axially extending, radially inwardly facing arcuate inner surface of one of the retention elements. The wheel flange is inserted with its supporting leg and the wheel body remaining out of contact with the shroud segment and with the wheel flange remaining out of contact with the platform. The inner surface is ground through contact with an annular outer grinding surface of the wheel flange. The wheel leg and body remain out of contact with the shroud segment and the wheel flange remains out of contact with the platform during grinding.