A gas burner system for providing a thin, flat flame for use in a long narrow combustion space, has a first air supply plenum which has a long narrow rectangular cross-section, which is placed above a second plenum or combustion chamber of substantially the same cross-section. At the junction between the first and second plena there are longitudinal projections inwardly from both long walls of the second plenum, forming a long narrow rectangular inlet to the second plenum. A burner assembly comprising an elongated flattened pipe having a plurality of short air baffles welded on each side is supported in this narrow inlet to the second plenum and substantially in the center thereof. The overall width of the burner assembly is less than that of the inlet so that there are two longitudinal gaps between the burner assembly and the projections for the passage of combustion air. There are two sets of ports in the lower edge of the flattened pipe. A first set provides downstreamwardly and outwardly projecting ports for the passage of the major gas flow. A second set of smaller gas ports are drilled substantially laterally to the vertical, and the gas therefrom flows into the space behind the air baffles where a stable, sheltered flame can be provided, for continuous ignition of the major flow of gas issuing at high velocity from the first set of ports, and turbulently mixing with the air flow downwardly through the gaps. The walls of the second plenum and projections can be of conventional refractory material, or they can be of metal which is water cooled.