A brake unit, preferably for a rail vehicle, including in a housing: a piston, and a push rod in the form of a spindle in an axial slack adjuster. The axial directions of the piston and the push rod are substantially perpendicular to each other, and means are provided for force transmission between these parts. The force transmitting means includes wedge elements at the underside of the piston cooperating with a driver element coaxial with and force-transmittingly connected to the spindle. The driver element is supported with rolling friction by the housing for movements in the axial direction of the spindle, and the spindle is axially guided by the housing at its forward end.