It has been hypothesised that the stress distribution within the arterial wall may provide an indicator of atherosclerotic plaque disruption. Many studies have used patient specific finite element models to estimate the stress environment in atherosclerotic plaques, attempting to correlate the magnitude of stress to plaque vulnerability. This thesis investigates the accuracy of these stress measures as clinical indicators of plaque disruption and proposes two groups of novel measures, namely (i) the difference in curvature between the inner and outer plaque surfaces and (ii) the degree of required fibre remodelling during disease progression. To achieve these goals, patient specific geometries of the carotid bifurcation were developed from computerised tomographic angiography and excised plaques were tested to create material constitutive models. A remodelling algorithm was developed to predict the fibre architecture within complex geometries and thus infer an accurate anisotropic response for the arterial tissue. The fibre remodelling algorithm successfully predicted the complex fibre architecture which exists at arterial bifurcations, verified by comparison to experimental observations. Both groups of novel indicators proved useful in the identification of plaques vulnerable to disruption when assessed by comparing values of these indicators in symptomatic and asymptomatic vessels.