Abstract: The covering is constructed on the site and adheres to a corrugated support 1 and to spaced-apart projections 2. It comprises a reinforcing element of metal or of a glass cloth 4, 6 having meshes which are small enough to retain a foaming product which is still in the liquid state but sufficiently rigid (for example ribbed) so as to be planar and have great strength. The reinforcing element is embedded in the foaming material in the course of the solidification of the latter and imparts thereto a planar outer surface. Air pockets are formed between the corrugation roots 10 and the solidified and reinforced foaming product. This reinforcing element may include two successive layers, namely a layer 4 having small meshes and a layer 6 having large meshes, the latter providing the desired strength.