A new structural model is described for the tension-radius relationship of blood vessels, taking into account their mechanically important constituents: collagen, elastin and smooth muscle. The model has four characteristic parameters: EC, the Young's modulus of the collagen fibres; ESE, the Young's modulus of the combined smooth-muscle/elastin network; epsilon mu, the amount of strain at which the high stiffness region on the tension-radius curve is reached, and eta an indicator for the degree of collagen fibre stretching. The structural stiffness of the wall constituents is reflected by EC and ESE whereas the global stiffness of the entire blood vessel is described by epsilon mu and eta. All these elasticity parameters are pressure independent, in contrast to generally quoted values for the incremental modulus or vascular compliance which are strongly pressure dependent. Hence, an objective comparison of the mechanical properties for various types of blood vessel, based on the present model parameters, has been made possible. The model was successfully fitted to tension-radius data of 65 human aortas, age range 30-88 years, with moderate or severe atherosclerosis. The structural as well as the global stiffness changes with age, e.g. collagen stiffness shows a ninefold increase over 60 years. Global stiffness depends on atherosclerosis.