It has been extensively documented that changes in blood flow induce vascular remodeling and this phenomenon seems to be correlated to the shear forces imposed on the vessel wall by motion of blood. Wall shear stress, the tractive force that acts on the endothelium, has been shown to influence endothelial cell function. To study changes in wall shear stress that develop on the vessel wall upon changes of blood flow, we set up a technique that allows estimation of shear stress in the radial artery of patients on chronic hemodialysis therapy. The technique is based on color-flow Doppler examination of the radial artery before and after surgical creation of radiocephalic fistula for hemodialysis. Calculation of time function wall shear stress and blood flow rate in the radial artery is performed on the basis of arterial diameter, center-line velocity waveform and blood viscosity, using a numerical method developed according to Womersley's theory for pulsatile flow in tubes. The results presented confirm that the model developed is suitable for calculation of the wall shear stress that develops in the radial artery of patients before and after surgical creation of an arteriovenous fistula for hemodialysis. This methodology was developed for characterization of wall shear stress in the radial artery but may be well applied to other vessels that can be examined by echo-Doppler technique.