A device for milling a profile of a rail track intended for rail-bound vehicles includes at least one milling body that is capable of being driven in a rotationally movable manner about an axis of rotation, and a plurality of cutting plates attached to the at least one milling body. At least some of the cutting plates are capable of being pretensioned non-positively for fixing in a respective receiver by at least one clamping body against an abutment as a stop. The at least some of the cutting plates are capable of being deflected in the respective receiver in a radial and/or axial direction by an adjusting means and are capable of being fixed in an adjusted position by the clamping body. The adjusting means is configured to be movable and/or deformable by a pressure transmission fluid.