In this paper we present a technique to generate accurate computer models of the vascular system directly from multi-modality image data. When fully validated, the models will make it possible to analyze the vascular system more completely. For example, computer models can be used for monitoring vessel sizes in pre- and post-operative studies, or can serve as the basis for performing complex fluid flow analysis. Furthermore, incorporating physical properties such as the vessel elasticity into the models would allow for their use in a surgical planning environment. In creating the computer models, we have developed a multi-step process incorporating several techniques commonly found in many other computer vision problems. The process includes four steps: segmentation, thinning, directed graph formation, and surface construction. In this paper each of these techniques and their details are presented.