Abstract: The flexible hood (1) is movable between an extended position in which it covers the passenger compartment of the motor vehicle and a folded non covering position in which it is housed in a compartment (9) of the motor vehicle covered by a rigid lid (8). The lid (8) has recesses (12) at each end of its front edge (11) for avoiding interference between the lid (8) and the framework (2) of the hood (1), when the latter is unfolded.The recesses (12) are provided with covering elements (13) movable between an extended position, assumed when the flexible hood (1) is folded in the compartment (9), and a retracted position assumed when the flexible hood is unfolded.