a method is provided for producing an engine wall structure that includes an inner wall , to which hot gas is admitted during engine operation , an outer wall , which is colder than the inner wall during engine operation , and at least two webs that connect the inner wall with the outer wall and delimit a cooling duct between the walls . the engine wall structure is produced by wire - electro discharge machining the duct out of a solid sheet forming the entire engine wall structure including the inner wall , the outer wall and the webs .