A starting device has a friction element arranged between an engine and wheels for transmitting torque between them. The engagement and disengagement of the element is shifted by press force outputted from a press force applier, which is controlled by a control unit. The control unit includes a creep demand degree judging means judging a driver's creep demand degree for starting a motor vehicle after substantial stop of the vehicle with applying brake force to the wheels and outputs a creep demand degree signal, a creep time setting means setting creep time based on the creep demand degree signal and outputs a creep time signal, and a creep torque producing means producing creep torque by controlling the press force to obtain a slipping state of the element for a period determined based on the creep time signal.