A method for deploying an endoluminal vascular prosthesis using a deployment catheter that has at least a main graft portion and a first branch graft portion. The deployment catheter preferably comprises an elongate, flexible catheter body having a proximal end and a distal end, and an outer sheath and an inner core that is axially moveable with respect to the outer sheath. The catheter preferably comprises a main graft restraint that has a main graft release mechanism comprising a main graft sheath and a suture threaded through a plurality of the openings in the main graft sheath. The catheter further comprises at least one branch graft restraint comprising at least one branch graft release mechanism.