Steel charges are heated to rolling temperature in reheating furnaces. It is standard practice for the charge to be moved through such a furnace on continuous water-cooled tubular supports crossing the furnace in a straight line. The supports obstruct charge heat-up to the desired temperature at the points where the charge is in contact with the tubular supports. A lateral offset of the tubular supports or similar designs have been unable to overcome this disadvantage. The tubular supports of the present reheating furnace are therefore several times offset from a straight line through the furnace between the furnace inlet and the furnace exit or, in the case of a furnace with a fixed hearth in the soaking zone, the furnace inlet and the fixed hearth. Each tubular support section between two such offsets is shorter than the upstream tubular support section. The present arrangement is particularly advantageous for pusher-type furnaces or walking-beam furnaces.