Abstract: A safety brake for braking a moving member includes at least one active member co-operating by friction with a passive member. The active member is kept at a distance from the passive member by an incompressible fluid which opposes the effect of a drive element (7) that is coupled to the active member and tends to urge the active member against the passive member. The incompressible fluid is enclosed in a circuit (6) which possesses a frangible portion (8) such that when the frangible portion is broken in order to activate the safety brake, it constitutes an exhaust opening to allow the incompressible fluid to escape from the circuit (6).