Abstract: An improved flat roof structive is provided comprising a substructure and a plurality of insulating elements which are loosely positioned on the substructure. A corrugated cover member of a substantially rigid material is positioned on the insulating elements at least in an area adjacent the outer perimeter of the roof. The corrugated cover member has downwardly facing channels which extend in a direction generally from an outer perimeter towards the center of a roof. The channels are open at their ends facing the perimeter of the roof and are closed or sealed at their ends facing toward the center of the roof. A strong air flow will create a vacuum under the cover member in wide areas which reduction is greater than the vacuum on the upper surface of the cover member whereby the cover member is pressed downwardly against the insulating elements. Due to the nearly uniform vacuum under the cover member, i.e.