Abstract: A roof covering or wall covering for a building or the like comprising a supporting layer having open channels, preferably made of corrugated metal sheet. Encasing structures, filled with a fire-retarding substance, are located in the channels of the supporting layer. The fire-retarding substance is a thickened liquid. Since the liquid is thickened, it cannot escape or can escape only very slowly from leaky points in the supporting layer in the event of fire. This ensures an evaporation of the fire-retarding liquid to remove the thermoenergy produced during the fire.