Measurement of stenosis due to atherosclerosis is essential for interventional planning. Currently, measurement of stenosis from magnetic resonance angiography (MRA) is made based on 2D maximum intensity projection (MIP) images. This methodology, however, is subjective and does not take full advantage of the 3D nature of MRA. To address these limitations we present a deformable model for reconstructing the vessel surface with particular application to the carotid artery. The deformable model is based on a cylindrical coordinate system of a curvilinear axes. In this coordinate system, the location of each point on the surface of the deformable model is described by its axial, circumferential and radial position. The points on the surface deform in the radial direction so as to minimize discontinuity in radial position between adjacent points while maximizing the proximity of the surface to local edges in the image. The algorithm has no bias towards either narrower or wider cross- sectional shapes and is thus appropriate for the measurement of stenosis. Axes of the vessels are indicated manually or determined by axes detection methods. Once completed, the surface reconstruction lends itself directly to 3D methods for measuring cross-sectional diameter and area.