Three-dimensional (3D) medical imaging has been incorporated in routine clinical practice, since the required infrastructure has become increasingly affordable. New algorithms and applications are needed to serve the additional image processing and analysis functions in 3D space. In this work we propose a system for semi-automatic modeling and segmentation of elongated salient and anatomical objects in 3D medical images. The proposed methodology is based on a novel mathematical formalization of a well-known class of geometric primitives, namely generalized cylinders (GCs), which exhibits advantages over the existing parametric definition. Since the anatomical objects have to be modeled by their intersection with the transverse image planes, the proposed methodology includes also a new seeded region growing (SRG) segmentation algorithm for ellipse detection in 2D images, based on a priori shape knowledge. Finally, the resulting GC model is used to initialize an active surface (AS) segmentation method, in order to accurately delineate the required object. In this work we present the proposed algorithms in detail, along with the evaluation of the accuracy of the model-based segmentation by experts. Results show that elongated objects like the aorta and the trachea may be segmented with sensitivity between 90% and 95%. The proposed SRG-ellipse detector requires minimal user-initialization and its executions requires only few seconds for each image slice on an average laptop. The evolution of the AS requires less than one second per iteration for a typical CT image. Comparisons are provided with state of the art semi-automatic medical image processing software, which validate the merit of the proposed work.