Abstract: A cooling system is disclosed for cooling the platforms of turbine blades fixed to the periphery of a turbine rotor, each turbine blade having an airfoil portion, a platform with opposite longitudinal edges, a root portion affixed to the turbine rotor, and a shank portion connecting the root portion to the platform. Adjacent turbine blades are located such that a longitudinal edge of one platform is adjacent to a longitudinal edge of an adjacent platform. A cavity is formed bounded by a portion of the periphery of the turbine rotor, the shank portions of the adjacent turbine blades, and the platforms of the adjacent turbine blades. A cooling air passage supplies cooling air to the cavity. One or more cooling channels are formed in a side of the platform facing the turbine rotor, each cooling channel having a cooling air collector at an end located adjacent to the air supply passage and communicating with the cavity.