This work presents the modelling and simulation of the mechanical behaviour of the human aortic arch under in vivo conditions with pressure levels within the normal and hypertension physiological range. The cases studied correspond to young and aged arteries without cardiovascular pathologies. First, the tissue of these two groups is characterised via in vitro tensile test measurements that make it possible to derive the material parameters of a hyperelastic isotropic constitutive model. Then, these material parameters are used in the simulation of young and aged aortic arches subjected to in vivo normal and hypertension conditions. Overall, the numerical results were found not only to provide a realistic description of the mechanical behaviour of the vessel but also to be useful data that allow the adequate definition of stress/stretch-based criteria to predict its failure.