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The cerebral tissue requires a constant supply of oxygen and nutrients. This is maintained through delivering a constant supply of blood. The delivery of sufficient blood is preserved by the cerebral vasculature and its autoregulatory function. The cerebral vasculature is composed of the Circle of Willis (CoW), a ring-like anastomoses of arteries at the base of the brain, and its peripheral arteries. However, only 50% of the population have a classical complete CoW network. This implies that the route of blood flow through the cerebral vasculature is different and dependent on where the blood is needed most in the brain. Autoregulation is a mechanism held by the peripheral arteries and arterioles downstream of the CoW. It ensures the delivery of the essential amount of cerebral blood flow despite changes in the arterial perfusion pressure, through the vasoconstriction and vasodilation of the vessels. The mechanisms that control the vessels’ vasomotion could be attributed to myogenic, metabolic, neurogenic regulation or a combination of all three. However, the variations in the CoW structure, combined with different pathological conditions such as hypertension, a stenosis or an occlusion in one or more of the supplying cerebral arteries may alter, damage or abolish autoregulation, and consequently result in a stroke. Stroke is the most common cerebrovascular disease that affects millions of people in the world every year. Therefore, it is essential to understand the cerebral hemodynamics via mathematical modelling of the cerebral vasculature and its regulation mechanisms. This thesis presents the developed model of the cerebral vasculature coupled with the different forms of autoregulation mechanisms. The model was developed over multiple stages. First, a linear model of the CoW was developed, where the peripheral vessels downstream of the CoW efferent arteries are represented as lumped parameter variable resistances. The autoregulation function in the efferent arteries was modelled using a PI controller, and a metabolic model was added to the lumped peripheral variable resistances. The model was then modified so the pressure losses encountered at the CoW bifurcations, and the vessels’ tortuosity are taken into account resulting in a non-linear system. A number of cerebral autoregulation models exist in the literature, however, no model combines a fully populated arterial tree with dynamic autoregulation. The final model presented in this thesis was built by creating an asymmetric binary arterial vascular tree to replace the lumped resistance parameters for the vasculature network downstream of each of the CoW efferent arteries. The autoregulation function was introduced to the binary arterial tree by implementing the myogenic and metabolic mechanisms which are active in the small arteries and arterioles of the binary arterial tree. The myogenic and metabolic regulation mechanisms were both tested in the model. The results indicate that because of the low pressures experienced by the arterioles downstream of the arterial tree, the myogenic mechanism, which is hypothesised by multiple researchers as the main driver of autoregulation, does not provide enough regulation of the arterioles’ diameters to support autoregulation. The metabolic model showed that it can provide sufficient changes in the arterioles’ diameters, which produces a vascular resistance that support the constancy of the autoregulation function. The work carried out for this research has the potential of being a significant clinical tool to evaluate patient-specific cases when combined with the graphical user interfaces provided. The research and modelling performed was done as part of the Brain Group of the Centre of Bioengineering at the University of Canterbury.