Apparatuses and methods for removing veins, usually varicose veins, rely on endoluminal capture of a distal end of the vein segment to be removed. In the illustrated embodiments, a shaft having reciprocatable penetrating elements is used to engage and capture the distal end of the vein. After rotating the shaft to pull the distal segment of the vein away from the connecting tissue, the shaft is withdrawn proximally, invaginating the segment back to the point of insertion.