This paper comprises a study of the secondary flow patterns that can develop in the human aortic arch. Clinical evidence of these secondary flows has been obtained by Kilner et al. using magnetic resonance velocity mapping techniques. Some of their results are presented for comparison in this paper. Four difference parametric models of the aortic arch have been analysed using computational fluid dynamic techniques. Both steady and transient flow conditions have been considered and two different commercially available software packages were used, namely FIDAP and FLOTRAN. A satisfactory comparison of the theoretical analysis with the results, both in vivo and in vitro, obtained by Kilner et al. for their out-of-plane inlet model was found. The theoretical analysis can now be extended to analyse the effect of different configurations and orientations of artificial aortic valves on the resulting aortic arch flow patterns.