A stent graft (10) has a tubular body of a biocompatible material and a side arm (20) fastened to the tubular body. A tubular extension piece (24) is sealingly joined to the end of the side arm and extends from it. It can be joined with adhesive or stitching. The extension piece can be formed from an elastomeric biocompatible material such as Thoralon™. The extension piece can have a resilient reinforcement 44 embedded into it and extending longitudinally. The extension piece is tucked back into the side arm during deployment of the stent graft into a body lumen.
