A technique is proposed for modeling the surface of normal cerebral vasculature based on three-dimensional magnetic resonance images. The Frangi multiscale image filtering is the starting point, followed by thresholding and skeletonization. The skeleton of tubular branches is approximated by a smooth function in 3D, allowing accurate estimation of tangent vector to the vessel centerline and planes normal to it. Vessel radius is then computed by least-squares fitting of the image intensity model to vessel cross-sections by normal planes. In effect, each tubular branch of the vessel tree is represented by centerline-radius description. The usage of Frangi filtering results in tubular branch discontinuities in places where the vessels do not feature the assumed elongated shape, e.g. at bifurcations and intensity artefacts. This paper proposes algorithms for modeling the vessel tree surface discontinuities. The resulting integrated surface of the macroscale (of diameter comparable or larger than the voxel side) vessels model is waterproof. This is important for future usage of the model for blood flow simulation. A network of mesoscale vessels (of diameter smaller than the voxel side) is synthesized at the branch terminations of the macroscale surface model, using constrained numerical optimization. This is a step toward modeling the whole brain vasculature.