A device for occluding a vessel employs one of a number of different expansion members joined to one or more elongate members. The expansion member may include a braid, one or more coils, ribs, a ribbon-like structure, a slotted tube, or a filter-like mesh. If the expansion member is enclosed by a suitable membrane, the device seals with the vessel wall to partially or completely occlude the vessel. A perforated membrane may be used to permit the perfusion of blood. The expansion member may be self-expanding, or it may be expanded by engaging it with one of the elongate members. Alternatively, the expansion member may be expanded by heating it.