Vessel curvature or tortuosity has usually been ignored in haemodynamic studies of the vasculature, vessels are commonly assumed to be straight and axisymmetric. This assumption is generally not valid and even for those vessels which are relatively straight in early life, such as the abdominal aorta, there is a tendency to develop tortuosity with increasing age. This paper proposes a quantitative evaluation of tortuosity based on the standard deviation of the incremental displacements of the midline of a vessel. The tortuosity coefficients for the abdominal aorta were determined from the aortograms of 92 patients. For the majority of patients aged less than 40 years of age, the tortuosity coefficients were close to those expected for a straight vessel, i.e. less than 0.20. Above that age there is a rising incidence of tortuosity with, in some cases coefficients several times greater than those expected for the straight vessel case. This tortuosity is likely to be due to an aging of the vessel wall leading to loss of longitudinal stiffness. The haemodynamic implications of tortuosity are that it is likely to create flow profile asymmetries leading to abnormal wall shear stress and predispose the vessel to atherosclerosis. As a consequence tortuosity may be considered as a geometrical risk factor in the development of the disease.