Multi-disc brake, of the type incorporating at least one first rotary disc firmly fixed to the wheel of the vehicle and a second rotary disc mounted so as to slide on a support component itself firmly fixed to the wheel, the driving in rotation of the second disc by the said support component being effected by the intermediary of complementary splines having a gear tooth profile. To overcome the undersirable effects of the tilting moment exerted on the sliding disc (2) by the thrust of the actuating cylinder (12), the invention is arranged to provide this disc with axial guiding projections (14) engaging in openings of corresponding shape (15) arranged in the other disc (1).