A multiple-sided valve for implantation within a body vessel comprising a frame comprising a bioabsorbable material is provided. The devices can be pushed from a delivery catheter into the lumen of a duct or vessel and may include one or more barbs for anchoring purposes. A full or partial covering of fabric or other flexible material, or a bioabsorbable material, including a collagen-based material such as small intestinal submucosa (SIS), may be attached to the frame to form an occlusion device, a graft, or an implantable, intraluminal valve such as for correcting incompetent veins in the lower legs and feet.