Covering device for a motor vehicle having a foldable flat structure including a plurality of flat elements connected together in an articulated manner and displaceably guided on at least one guide device between a covered position in which the flat structure at least partially covers a receiver space and an uncovered position in which the flat structure at least partially uncovers the receiver space. The at least one guide device includes at least one control region, with different guide elements of the flat elements being path-controlled differently thereon, such that in the uncovered position the flat elements are pivoted at an angle to one another and the flat structure is folded in the manner of a concertina. A flexible covering structure is provided, the flexible covering structure at least partially spanning the flat elements and forming a visible surface of the foldable flat structure.