An apparatus for handling and orienting elastic, thin-walled, tubular members having a closed end and an open end, such as finger cots, such that all tubular members are delivered in the same orientation, the apparatus having a retrieval conduit, a delivery conduit angularly joined to the retrieval conduit, a reversing chamber extending linearly forward from the retrieval conduit and across the opening to the delivery conduit, and suction means to draw the tubular members through the retrieval and delivery conduits. A tubular member traveling in the forward orientation with the closed end forward will be drawn directly into the delivery conduit, while a tubular member traveling in the reverse orientation with the open end forward will first pass the opening to the delivery conduit and strike the barrier end wall of the reversing chamber, and then be drawn into the delivery conduit with the closed end forward.