Compliant (flexible) structures play an important role in several biofluid problems including flow in the lungs, heart and arteries. Atherosclerosis is a vascular disease which causes a remodelling of the arterial wall causing a restriction (stenosis) by thickening the intima and the formation of vascular plaque by the deposit of fatty materials. This remodelling alters the compliance of the artery stiffening the arterial wall locally. A common location for this to occur is in the carotid artery which supplies blood to both the brain and the face. It can lead to complete occlusion of the artery in the extreme case and is a major cause of stroke and ischemic infarction. Stroke is the third largest cause of death in the U.S.A., but even if not fatal it can cause coma, paralysis, speech problems and dementia. Atherosclerosis causes a change in the local hemodynamics. It can produce areas of flow separation and low wall shear stress, which can lead to endothelial dysfunction and to promotion of plaque growth. In-vitro modelling with artificial flow phantoms allows the fluid mechanics of the circulatory system to be studied without the ethical and safety issues associated with animal and human experiments. Extensive work has been performed using both experimental and computational techniques to study rigid models representing the arterial system. Computational methods, in which the equations governing the flow and the elastic walls are coupled, are maturing. There is a lack of experimental data in compliant arterial systems to validate the numerical predictions. This thesis sets out to address the problems associated with the in vitro experimental analysis of compliant structures representing the human vasculature. A novel construction technique that produced idealised compliant geometries representing both a healthy and stenosed carotid artery from transparent silicone material was developed. A complete analysis was performed of the circumferential and longitudinal response of the geometry, which allowed for dynamic similarity between in vitro and in vivo conditions to be achieved. Inherent difficulties associated with thin walled phantom construction were overcome, which included the design of a novel endplate that allowed for a smooth transition from the flow system to the flow phantom and a bottom up silicone injection system that ensured the phantom was free of bubbles. The final phantom evolution had a wall thickness that could be produced to within a tolerance of 5%. The constructed flow phantom was ported to a flow system producing a physiological inlet flow waveform scaled to in vitro conditions via Reynolds and Womersley number matching. Experimental analysis was performed using a laser based optical technique, particle image velocimetry (PIV). A novel Light Emitting Diode (LED) illumination system was also implemented to obtain to obtain high speed planar PIV measurements. The combined set up of the LED light source, driver unit components and fibre optics for high speed imaging costs in the region of $US 650 which provides a far cheaper option in comparison to the pulse laser system (In the region of $US 50,000). Results obtained in the healthy geometry were compared to a rigid geometry with the same dimensions. It was found that compliance reduced the peak velocity experienced. It also caused a reduction in wall shear stress (WSS) observed and acted to ameliorate the magnitude of the WSS. This is physiologically significant as high WSS can promote atherosclerosis. The introduction of a stenosis caused an increase in the peak velocity observed over the cardiac cycle. A large increase in WSS can be seen to occur in the stenosis throat in both a symmetric and asymmetric stenosed geometry. It is also evident that stenosis eccentricity is important, with asymmetry (where the centre of the stenosis does not coincide with the centre of the artery) producing a major change in WSS and flow field. The study of the flow field downstream of a symmetric stenosis exit showed a Kelvin-Helmholtz vortex ring system to occur between the jet exiting the stenosis throat and the low velocity reverse flow region that surrounded it. The strength of these vortices varied between the acceleration and deceleration phase, demonstrating the failings of a quasi-steady assumption. It was shown that varying the external pressure applied to the flow phantom, along with stenosis eccentricity, affected the inlet flow and pressure waveform and the failings of the common assumption to idealise the physiological flow wave with a sinusoidal input was presented.