An intravascular cuff acts as a lining between a native vessel and an intravascular prosthetic device. During deployment, the ends of the cuff curl back upon themselves and are capable of trapping native tissue, such as valve leaflet tissue, between the ends. The cuff creates a seal between the vessel and the prosthetic, thereby preventing leakage around the prosthetic. The cuff also traps any embolic material dislodged from the vessel during expansion of the prosthetic.