The hydraulic antivibration support has two rigid strength members interconnected by a bell-shaped elastomer body, a flexible elastomer wall connected to the second strength member, and a rigid partition secured to the second strength member and defining both a working chamber on its elastomer body side and a compensation chamber on its flexible wall side. These two chambers are filled with liquid and are connected to each other via a narrow channel, via a central nozzle fitted with an axially movable shutter, and via an annular flap disposed around the central nozzle between two grids. One of the grids is axially slidable and is connected to the shutter so as to block the flap when the shutter is open.