Abstract: Methods of making cylindrical structures with cooling channels, such as, for example, combustor/transition pieces for gas turbines having a double wall with a plurality of cooling channels, both axially and, in some cases, circumferential cross-flow passages positioned between the structure's inner member and the outer member to provide cooling air thereto, are disclosed. The cooling channels are formed in the area between the inner member of the structure and the outer member thereof. The passages preferably extend both axially and circumferentially with respect to the direction of flow through the structure. The axial passages extend completely from one end to the other and the circumferential passages extend around the circumference of the structure.