The invention relates to a brake by-wire actuator for actuating the braking system of a motor vehicle, comprising at least one simulator (2) which can be impinged upon by a brake pedal (1), a signal of the actuation sensor (3) being supplied to an electronic control unit (4) which controls a pressure source according to the signal of the actuation sensor (3), one output of the pressure source being connected to a distributor device (10) for the braking force, and actuates individual wheel brakes (16) of the vehicle. Means are also provided to enable actuation of the brakes by muscular power within a recoil plane. In order to provide an improved recoil plane in a brake-by-wire actuator of the above-mentioned variety, free travel (a) is foreseen between a first actuation component (47), such as a brake pedal (1) or a component (36;21) connected thereto, and an actuation component (37) located downstream in the force flow such that the first actuation component (47) can be mechanically decoupled from force reactions occurring in the vehicle braking system in a by-wire mode.