Brake master cylinder (10) for a motor vehicle, of the type which comprises a substantially axial body (12) inside a bore (14) of which at least one axial piston is slideably mounted, of the type in which the bore (14) comprises two seals, front (30, 34) and rear, interposed between the piston and the bore (14), the seals (30, 34) comprising three radially concentric lips accommodated in grooves (70, 72) in the bore (14), characterized in that front faces of the grooves (70, 72) are configured at least in part as a slope.