One embodiment according to the present invention includes an occlusion device in which the support structure or frame expands circumferentially within the lumen to secure an expansile plug or embolic material. Once in place, the expansile plug or embolic material expands, thereby occluding the target lumen. Another embodiment according to the present invention includes a radially expandable support structure having a closed portion for capturing subsequently delivered embolic material, such as embolic coils. For example, the structure may have a closed portion at its distal end or at its middle (forming an hourglass shape). Additionally, the closed portion may be formed from the support structure itself or from a discrete, second layer that is attached within the support structure.