Abstract: An air tight and fluid tight cover for padded bodies, mattresses and the like. The cover has a top, a bottom and a plurality of side parts. At least one opening provides ventilation between the interior of the cover and the ambient atmosphere. At least two of the side parts are formed by at least an interior, middle and exterior layer of material. Air passage openings offset with respect to each other are provided in the interior and middle layers of material. At least one filter is disposed between the middle and outer layer of material. A plurality of connecting seams extend partially transversely across the width of the side part from diametrically opposite points of the upper and lower longitudinal edges of the side parts toward a longitudinal center line bisecting the side part. The connecting seams define a plurality of pockets in which the filters are disposed. The connecting seams also define air passages between the individual layers of material for trapping coarse granular particles therein.