A joining arrangement between a main tube (3) and a side arm (5) in a side arm stent graft (1). The side arm (5) is stitched into an aperture (11) in the main tube and is in fluid communication with it. The aperture is triangular, elliptical or rectangular and the side arm is cut off at an angle to leave an end portion having a circumferential length equal to the circumference of the aperture. The side arm can also include a connection socket (76) comprising a first resilient ring (79) around the arm at its end, a second resilient ring (80) spaced apart along the arm from the first ring and a zig zag resilient stent (82) between the first and second rings. The zig-zag resilient stent can be a compression stent. Both the main tube and the side arm are formed from seamless tubular biocompatible graft material.