The invention relates to a vehicle (2) provided with a power-steering device (1) which includes at least one steering rack (3) and an assistance motor (4) arranged to drive said steering rack (3), as well as at least one on-board computer (13) inside the vehicle (2), intended for controlling said assistance motor (4), the computer (13) being placed mostly, and preferably entirely, below the rack (3), preferably in a shell (20), inside of which the rack (3) is translatably guided, and inside of which a space for the computer is arranged for said purpose.