A method for computer-aided assessment of blood vessel geometries based on shape-fitting algorithms from metric vision is evaluated. Acoustic images of cross-sections of the radial artery and the cephalic vein were acquired, and medical practitioners used a computer application to measure the wall thickness and nominal diameter of these blood vessels with a caliper method and the shape-fitting method. The two methods perform equally well for wall thickness measurements. The shape-fitting method is preferable for measuring the diameter, since it reduces systematic errors by up to 63 % in the case of the cephalic vein due to its eccentricity.