An intravascular cuff acts as a lining between a native vessel and anintravascular prosthetic device. During deployment, the ends of the cuff curlback upon themselves and are capable of trapping native tissue, such as valveleaflet tissue, between the ends. The cuff creates a seal between the vesseland the prosthetic, thereby preventing leakage around the prosthetic. The cuffalso traps any embolic material dislodged from the vessel during expansion ofthe prosthetic.