A gripping device (10) is operative within a body vessel which includes an elongate, flexible support body (12) having a plurality of spaced gripping members (22) attached to the support body to extend axially outwardly from the outer end thereof. The gripping members are formed to have an expansion position where they angle laterally from the support body. A cone shaped flexible liner (34) forming an open ended enclosure in the expansion position of the gripping members has an outer end connected to the distal ends (26) of the gripping members, and an inner end connected to the support body. The flexible liner is surrounded by the gripping members. The gripping members extend outwardly at a first angle relative to the longitudinal axis. The flexible liner has a first section adjacent an open end thereof inclined to the longitudinal axis at the first angle. A second section of the flexible liner extends from the first section to the support body at an angle relative to the longitudinal axis that is greater than the first angle.
