A catheter for use in an emboli containment system includes a flexible elongate member having self-expanding sealing means mounted on its distal extremity. This self-expanding sealing means can take any suitable form, such as a braided structure formed of a suitable shape memory material such as a nickel titanium alloy. In order to prevent abrasion of a vessel, it is desirable to cover the braided structure with a covering of a suitable material such as a polymer which extends over the braided structure and which moves with the braided structure as it expands and contracts.