Abstract: A turbine blade includes a longitudinally extending cavity into which air for cooling the interior wall of the blade is admitted. The air passes from the cavity through each of a group of inserts each of which is constituted by a plurality of stepped overlapping walls with spaced air passages therethrough, these walls establishing therebetween corresponding cooling spaces interconnected by the passages and which are bounded at one side by the blade wall. The cooling air passes in succession through the cooling spaces of each insert and is discharged from the insert and thence from the blade through an outlet port formed in the blade wall and which is connected to the last cooling space of each insert through which the air is passed. The passages through the overlapping walls also provide impingement cooling of the blade wall. The outlet ports for the cooling air are formed in the suction side of the blade as well as in its trailing edge.