An elastic mounting ring installation tool for connecting braces to brackets attached to the teeth of a patient has a housing with a barrel section, at the front end of which a magazine holder with a magazine provided with elastic rings for placement onto brackets provided on the teeth is arranged for mounting the braces to the teeth by the elastic mounting rings and a rod with wire fingers is movably supported in the barrel section for scooping up the elastic rings and transferring them to tooth brackets of the patient. The magazine holder is supported so as to be movable away from the wire fingers in a direction normal to the axis of the rod for pulling an elastic ring engaged by the wire fingers in a sideward direction for disconnecting the elastic ring from the magazine.