Provided is an arrangement for stowing away a retractable tonneau cover assembly (50) under a floor of a luggage space (10) requiring a very small space. A recess (36) is formed laterally across a width of a vehicle body in a rear end thereof. When stowing away the assembly, an outer tube (52) of the assembly is received in the recess with a longitudinal slot (54) thereof facing upward. A flexible cover sheet (56) extends out of the longitudinal slot (54), and a rigid free end member (58) attached to a free end of the flexible cover sheet (56) extends along a rear side of the outer tube into a deep section (36B) of the recess (36). Therefore, the recess (36) is required to have a width which is not significantly greater than the height (h) of the outer tube (52).