[Problem] To provide a radiant wall burner unit with which a processed material can be more uniformly heated and the size of the furnace can be reduced. [Solution] A radiant wall burner unit equipped with a furnace body element (5) that forms a radiant wall surface Z which faces the processed material, and a pair of regenerative burner devices (7) that form a flat flame f along the radiant wall surface of the furnace body elements and heat the radiant wall surface, with the processed material being heated by radiant heat from the radiant wall surface. The burner devices are equipped with apertures (9), which are formed by opening holes in the furnace body element and through which the flat flame is emitted, and air flow paths (8), which are formed in the furnace body element and are connected to the apertures, and through which combustion air C is circulated. The air flow paths and the radiant wall surface are connected by a continuous curved surface S via the apertures. Consequently, the flat flame flows along the entire radiant wall surface due to the airflow of the combustion air, which generates the Coanda effect.