An endoluminal device for affixation to a wall of a body lumen having a neck region defined by a relatively narrow width and a shoulder region that diverges from the neck region to a relatively wider width. The device comprises a shoulder portion, which may be part of a bulbous portion, having a diameter profile that conforms to the shoulder region, and, in some embodiments, a plurality of affixation members in an area of the device that typically extends from a distal end of the device through the shoulder portion. In one embodiment, the device comprises an endograft for repair of an aneurysm, such as an abdominal aortic aneurysm (AAA). Methods of using the endograft to inhibit continued diametric expansion of the aneurysm and to inhibit endoleak formation and migration of the endograft are also described.