A wall structure for a gas turbine engine structure, such as a combustion chamber or an afterburner duct is disclosed having a plurality of cooling orifices formed through the wall located in a plurality of odd and even transverse rows, each row having a plurality of cooling orifices located in a plane extending substantially perpendicular to a longitudinal axis of symmetry with the cooling orifices of each odd and even row being circumferentially offset from the cooling orifices of the adjacent upstream corresponding odd and even row. The cooling orifices have a common diameter D and are circumferentially offset a distance d such that distance d is between 0.5 D and D. The axes of the orifices in the odd numbered rows lie on a first main line extending obliquely to the longitudinal axis of symmetry and to the oxidizer air flow, and the axes of orifices on the even numbered rows lie on a second main line, also extending obliquely to the longitudinal axis of symmetry and to the oxidizer air flow. The axes of the orifices in the adjacent rows lie on secondary lines which extend obliquely to the first and second main lines and also to the longitudinal axis of symmetry. Any weld joints necessary to form the annular combustion chamber or afterburner duct from a plurality of wall segments extend parallel to the secondary lines and may be spaced equidistantly from adjacent secondary lines.