Arteries are living tissues which react and adapt to their environment, particularly in relation to changes in the rate of blood flow required to supply peripheral tissues or organs. Medium and small size arteries increase in diameter in response to short-term demands for increased flow and decrease in diameter in the event of diminished demands. Such immediate reactions are regulated primarily by vasoactive substances acting directly on smooth muscle cells of the media or by release of smooth muscle relaxation or contraction factors elaborated by endothelial cells. Chronic or long-term changes in arterial diameter appear to be governed directly by near-wall flow phenomena, e.g. the fluid dynamic wall shear. Recent evidence suggests that the normal tendency of arteries to respond to long-term changes in the shear field can result in intimal thickening and that this response may also favor the development of atherosclerosis. Thus, there appears to be a close relationship between fluid dynamics and the structure of arteries. From the fluid dynamics viewpoint, the pulsatile, three dimensional nature of blood flow requires sophisticated experimental methods in order to provide adequate data for correlation with biological studies. Research within the past decade has led to the conclusion that arteries seek a vessel diameter-blood flow combination which results in a flow-induced mean wall shear stress of approximately 15 dynes/sq.cm. If this value is chronically exceeded, vessel enlargement develops. If normal baseline shear stress is not restored by this increase in radius, the local response may continue. Conversely, reduced wall shear tends to induce intimal thickening in order to reduce lumen radius and thus increase wall shear toward normal levels. Under certain conditions this reaction may progress to the development of atherosclerotic plaques. Despite this knowledge, key points remain to be clarified. Is it the wall shear stress or the wall shear rate which determines the reaction? The former possibility implies that a mechanical shear-related stimulus is at the heart of the biological response mechanisms while the latter suggests a mass transport-related mechanism.