Abstract: A mattress cover, for use on an air inflatable mattress which reduces the risk of bed sores in long term patients. The cover has a top sheet and side sheets attached to opposite edges of the top sheet. The length of the top sheet, in a laid-flat state, is greater than the length of the side sheets attached to the top sheet. This allows the cover to closely follow the undulating nature of the inflatable cells of the mattress, and zero pressure may be achieved. The cover may also comprise end sheets, an outer skirt, and a base portion. The present invention also provides a method of making cover, which comprises the step of stretching the side portions, while the top sheet is in a substantially unstretched condition, and then joining the side sheets in their stretched condition to the top sheet.