In the present study, the estimation of elastic modulus of large arteries is used as an index for arterial stiffness. At first, a dynamic model is introduced for pulsatile blood flow in arteries with elastic walls. The model is based on Navier-Stokes equations in fluid mechanics and the theory of elasticity. The system of equations is completed by clinical ultrasound data obtained from Doppler ultrasound images of carotid artery of 40 healthy male volunteers. For this purpose, Doppler ultrasound images are recorded and saved in computer and then center-line blood velocity, arterial wall thickness, and arterial radius measured by offline processing. The results from analytic solution of completed equations show that the mean elastic modulus for the group of healthy volunteers is about 213 kPa. By applying this method, non-invasive clinical evaluation of common carotid artery stiffness by Doppler ultrasound measurement will be possible, without the measurement of local blood pressure.