A covering device for surfaces or for windows, doors, or similar openings or zones or for surface portions of the aforementioned items, has at least one covering element, which has movable element parts joined in zigzag fashion and capable of being fanned out and closed like a fan, which can be fanned out into an approximately two-dimensional shape of the covering element and closed to make a stack, and the at least one covering element has two peripheral parts, which either are independent or are formed by parts of the covering element and which in the fanned-out state extend at an angle to one another and which in a common zone are at least essentially brought together, and the element parts in the common zone are held together forming approximately a stacked block, and the stacked block is embodied as an independently freely movable part.