The complexity and diversity of the vascular system makes it difficult to perform quantitative blood vessel modeling and analysis. Emerging applications in biomedical modeling, bio-mimetic manufacturing and tissue engineering necessitate the development of new approaches to computational modeling of vascular structures. In this paper, we address the computational representation of realistic vascular objects to enable deformable blood vessels. First, we construct a swept volume based vascular model from a physiological vascular model. Second, we construct the NURBS surface based on deformable circles, i.e., the primitive of swept volume, as the boundary of the swept volumes. The approach of NURBS surface construction can also be extended to reconstruct medical image based vasclar models. In the end, potential applications of the mathematical representation of vascular structure including blood flow simulation in scaffold are discussed. As a computational representation, our vascular model enables multiscale visualization of a realistic vascular system.