In the current clinical workflow of endovascular abdominal aortic repairs (EVAR) a stent graft is inserted into the aneurysmatic aorta under 2D angiographic imaging. Due to the missing depth information in the X-ray visualization, it is highly difficult in particular for junior physicians to place the stent graft in the preoperatively defined position within the aorta. Therefore, advanced 3D visualization of stent grafts is highly required. In this paper, we present a novel algorithm to automatically match a 3D model of the stent graft to an intraoperative 2D image showing the device. By automatic preprocessing and a global-to-local registration approach, we are able to abandon user interaction and still meet the desired robustness. The complexity of our registration scheme is reduced by a semi-simultaneous optimization strategy incorporating constraints that correspond to the geometric model of the stent graft. Via experiments on synthetic, phantom, and real interventional data, we are able to show that the presented method matches the stent graft model to the 2D image data with good accuracy.