Many clinical applications, such as surgical planning, require volumetric models of anatomical structures represented as a set of tetrahedra. A method of constructing anatomical models from medical images is presented. The method starts with a set of contours segmented from the medical images by a clinician and produces a model that has high fidelity with the contours. Unlike most modeling methods, the contours are not restricted to lie on parallel planes. The main steps are a 3D Delaunay tetrahedralization, culling of non-object tetrahedra, and refinement of the tetrahedral mesh. The result is a high-quality set of tetrahedra whose surface points are guaranteed to match the original contours. The key is to use the distance-map and bit-volume structures that were created along with the contours. The method is demonstrated on both computed tomography and 3D ultrasound data. Models of 170,000 tetrahedra are constructed on a standard workstation in approximately ten seconds.