A cabriolet vehicle with a roof provided which at least in some areas has a flexible cover, which includes in its front roof area a rigid area, a so-called roof top, overlapped by a cover. The front roof area can be stored in the same orientation as in the closed state in a body recess, and the body recess is bounded on the rear by an edge serving as a front edge of the additional body outer surface extending to the rear. The edge is preceded at least in parts of it area by a support step for a flexible lining running from the edge to an area of the roof. The step is adapted to the contour of the edge.