A motor vehicle roof configuration which can be put away has at least two shaping sections, which are movable relative to one another and can be put away together, for lateral convertible top cloth strips. The shaping sections lie in a row next to one another in a closed position of the roof configuration and have water channels which run approximately parallel to each convertible top cloth strip and in the longitudinal direction of the vehicle and also adjacent to the convertible top cloth strips. It is provided that, at least in a closed position of the roof configuration, an inner edge of each convertible top cloth strip together with at least one sealing configuration forms a leakproof covering for the adjacent water channel.