A fitted covering for a mattress includes a body, a peripheral elastic cord, and corner elastic bands. The body includes an upper panel and a side skirt extending outwardly away from the upper panel to define a free edge opposite the upper panel. The upper panel defines corners, and the side skirt defines corner lines each extending away from one of the corners of the upper panel. The peripheral elastic cord is coupled to and extends substantially coextensively with the free edge. The corner elastic bands are each formed separately from one another. The corner elastic bands each extend substantially transversely across and secured to a corresponding one of the corner lines of the side skirt. Each of the corner elastic bands is positioned nearer the peripheral elastic cord than the upper panel.