Abstract: Mattresses conventionally are covered by bed sheets having a size to extend beyond the borders of a mattress on which it is to be placed so that its projecting edges may be tucked under the mattress. It is often difficult to apply a sheet smoothly and, in particular when a person is resting or sleeping on the mattress, the sheet may be pulled out from under the mattress and be displaced. The invention suggests a mattress cover in the form of a sleeve, which includes a top sheet; two opposite end walls and two opposite elongated side walls joined to the top sheet. It has flaps extending from the end walls and side walls and a bottom sheet joined to the flaps. An elongated open section is provided between adjacent edges of the bottom sheet and a flap of one of the side walls and a flap of at least one of the end walls, defining an opening through which a mattress can be inserted into the sleeve.