Bronchoscopic biopsy of the central-chest lymph nodes is vital in the staging of lung cancer. Three-dimensional multi-detector CT (MDCT) images provide vivid anatomical detail for planning bronchoscopy. Unfortunately, many lymph nodes are situated close to the aorta, and an inadvertent needle biopsy could puncture the aorta, causing serious harm. As an eventual aid for more complete planning of lymph-node biopsy, it is important to define the aorta. This paper proposes a method for extracting the aorta from a 3D MDCT chest image. The method has two main phases: (1) Off-line Model Construction, which provides a set of training cases for fitting new images, and (2) On-Line Aorta Construction, which is used for new incoming 3D MDCT images. Off-Line Model Construction is done once using several representative human MDCT images and consists of the following steps: construct a likelihood image, select control points of the medial axis of the aortic arch, and recompute the control points to obtain a constant-interval medial-axis model. On-Line Aorta Construction consists of the following operations: construct a likelihood image, perform global fitting of the precomputed models to the current case's likelihood image to find the best fitting model, perform local fitting to adjust the medial axis to local data variations, and employ a region recovery method to arrive at the complete constructed 3D aorta. The region recovery method consists of two steps: model-based and region-growing steps. This region growing method can recover regions outside the model coverage and non-circular tube structures. In our experiments, we used three models and achieved satisfactory results on twelve of thirteen test cases.