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Cardiovascular disease, mostly atherosclerosis, is responsible for one third of all deaths globally, rising to more than 50% in the Western World. Risk factors include smoking, diet, and familial history. Doppler ultrasound can provide estimates of blood velocity and wall shear rate. Clinically, maximum velocity is used to categorise patients for surgery, although Doppler velocity measurement is prone to errors and in need of validation. Wall shear stress—which can be derived from wall shear rate—plays a role in disease initiation and progression, although its clinical utility is unclear due to difficulties associated with its measurement. This thesis investigates the use of Doppler ultrasound as a tool to estimate blood velocity and wall shear rate. A simplified method for estimation of wall shear rate in healthy arteries is developed that uses spectral Doppler ultrasound. This method is based upon the theory of oscillatory flow in rigid pipes, requiring two measurements that are readily available with clinical ultrasound machines. This method is compared to a similar method based on colour flow imaging. The spectral Doppler method underestimated the theoretic value of wall shear rate by between 7 and 22%, with results varying between phantoms. Errors for the colour method were on average 35% greater. Test measurements from one healthy volunteer demonstrated that this method can be applied in-vivo. In more advanced stages of disease, peak velocity distal to a stenosis is of clinical interest and the simplified method for wall shear rate estimation is invalid. Steady flow in a series of simplified stenosis geometries was studied using a dual-beam Doppler system to obtain velocity vectors. These measurements were compared with data from an equivalent system that used particle image velocimetry (PIV) and was considered the gold standard. For Reynolds numbers at the stenosis throat of less than 800, flow remained laminar over the region studied, although distal flow separation did occur. For higher throat Reynolds numbers—corresponding to more severe stenoses or increased flow rates—asymmetric recirculation regions developed; the transition to turbulence occurred more proximally, with a corresponding reduction in stenotic jet and recirculation length. Qualitative agreement was observed in the velocity profile shapes measured using ultrasound and PIV at throat Reynolds numbers less than 800. Above this threshold the qualitative agreement between the velocity profiles became poorer as both downstream distance and the degree of stenosis increased. Peak axial velocity distal to the stenosis was underestimated, on average, by 15% in the ultrasound system. Estimation of shear rate remained difficult with both experimental techniques. Under a Newtonian approximation, the normalised wall shear stresses agree qualitatively. Under pulsatile flow conditions using an idealised flow waveform, superior qualitative agreement was observed in the velocity profiles at diastole than at systole. Similar to the steady flow behaviour, this agreement deteriorated with stenosis severity. The current generation of clinical ultrasound machines are capable of estimating the wall shear rate in healthy arteries. In the presence of significant arterial disease, errors in the peak velocity may result in mis-selection of patients for surgery, while estimation of the wall shear stress remains extremely problematic; particularly with identifying the wall location and measuring velocities close to the wall.