A system for endoluminal delivery of a medical device, wherein the medical device includes a bifurcated stent graft having a trunk, a first leg and a second leg shorter than the first leg. The system includes a sheath having a tubular wall having a cylindrical inner surface defining a lumen for receiving the stent graft therein to constrain the stent graft toward a delivery configuration suitable for endoluminal delivery, and a generally cylindrical core member extending through the lumen. The core member has a first annular surface for engaging an end of the first leg. The core has a second annular surface for engaging an end of the second leg while at least the end of the second leg remains constrained by the sheath.
