A stent graft has a tubular side arm which can be angled proximally and distally and from side to side. The wall of the stent graft in the vicinity of the side arm has a loose fold of the graft material and the side arm is fastened to the loose fold of graft material. The tubular side arm has an inner end and an outer end and is fastened into the loose fold of graft material by a circumferential fastening around the tubular side arm between the inner end and the outer end so that the tubular side arm extends partially within the tubular body of the stent graft and partially outside the tubular body of the stent graft. The loose fold of graft material can be formed by the graft material defining a recess in the wall of the stent graft. To enable movement or angulation proximally and distally and from side to side the loose fold of graft material is provided both proximally and distally of the tubular side arm and circumferentially to each side of the tubular side arm.