We introduce a new model-based approach for the segmentation and quantification of the aortic arch morphology in 3-D computed tomography angiography (CTA) data for thoracic endovascular aortic repair (TEVAR). The approach is based on a model-fitting scheme using a 3-D analytic intensity model for thick vessels in conjunction with a two-step refinement procedure, and allows us to accurately quantify the morphology of the aortic arch. Based on the fitting results, we additionally compute the (local) 3-D vessel curvature and torsion as well as the relevant lengths not only along the 3-D centerline, but particularly also along the inner and outer contour. These measurements are important for preoperative planning in TEVAR applications. We have validated our approach based on 3-D synthetic as well as 3-D MR phantom images. Moreover, we have successfully applied our approach using 3-D CTA datasets of the human thorax and have compared the results with ground truth obtained by a radiologist. We have also performed a quantitative comparison with a commercial vascular analysis software.