A fabric packing has a plurality of layers made of a filament of metal or plastic and includes bulges for maintaining the fabric layers at a distance. The bulges have first protuberances of generally trough-shaped configuration and second protuberances formed on the first protuberances, thereby defining respective apexes. The second protuberances are sized smaller than the first protuberances, wherein neighboring fabric layers are supported on one another via the second protuberances.