The abdominal aorta (AA) in older individuals can develop an aneurysm, which is of increasing concern in our ageing population. The structural integrity of the ageing aortic wall, and hence aneurysm, depends primarily on effective elastin and multiple families of oriented collagen fibres. In this paper, we show that a structurally motivated phenomenological 'four-fibre family' constitutive relation captures the biaxial mechanical behaviour of both the human AA, from ages less than 30 to over 60, and abdominal aortic aneurysms. Moreover, combining the statistical technique known as non-parametric bootstrap with a modal clustering method provides improved confidence intervals for estimated best-fit values of the eight associated constitutive parameters. It is suggested that this constitutive relation captures the well-known loss of structural integrity of elastic fibres owing to ageing and the development of abdominal aneurysms, and that it provides important insight needed to construct growth and remodelling models for aneurysms, which in turn promise to improve our ability to predict disease progression.