Abstract: Polymeric sheets having on one or both sides a fabric texture and a network of elongated channels in the interior of the structural framework of the sheet. In one embodiment, the sheets comprise a plurality of interbonded continuous polymeric ribs extending in a direction parallel to the plane of the sheet. The ribs impart a fabric texture to both sides of the sheet and define between them recessed portions on each surface of the sheet. The elongated channels extend throughout the ribs. The open area between the ribs can vary from zero to 60%. In another embodiment, the sheets have an ultra-thin, pinhole-free silicone rubber membrane on one side and a fabric texture on the other side. The sheets are useful as burn coverings where they serve as synthetic temporary replacements for damaged or missing skin.