A fitted mattress cover is provided with a flat top panel and a knitted or woven fabric skirt attached to and depending from the periphery of the top panel. The lower edge of the skirt contains a band of longitudinally extending elastic yarns that were integrally incorporated into the edge during fabrication of the skirt fabric. The yarns of the elastic band provide sufficient tension to pull some of the skirt fabric under the mattress and provide a secure fit when the cover is installed on a mattress.