A motor vehicle hood lining for stiffening the hood in the vicinity of its periphery and co-operating therewith to form a hollow body over at least a fraction of its periphery, the lining being generally of channel section with a bottom and side walls. Said bottom or at least one of said side walls presents, at least locally, a zone of weakness that is dimensioned in such a manner that in the event of the hood impacting the head of a pedestrian, once the bottom of the hollow body has come to bear against a high hard point placed in the engine compartment, the zone of weakness breaks. The invention also relates to a combination of such a lining with various hard points in an engine compartment.