A turbine shroud segment attachment with a casing (1) and several shroud segments (2) arranged in the casing (1), wherein the individual shroud segments (2) are located in the casing (1) with a circumferential clearance (3) between the individual shroud segments (2), in that the clearance (3) is reduced to zero at a given temperature difference between the casing (1) and the shroud segments (2), and in that the shroud segments (2) are retained on the casing (1) by way of an elastically deformable locating arrangement.