Atherosclerotic lesions are non-uniformly distributed at arterial bends and branch sites, suggesting an important role for haemodynamic factors, particularly wall shear stress (WSS), in their development. The pattern of lesions at aortic branch sites depends on age and species. Using computational flow simulations in an idealized model of an intercostal artery emerging perpendicularly from the thoracic aorta, we studied the effects of Reynolds number and flow division under steady conditions. Patterns of flow and WSS were strikingly dependent on these haemodynamic parameters. With increasing Reynolds number, WSS, normalized by the fully developed aortic value, was lowered at the sides of the ostium and increased upstream and downstream of it. Increasing flow into the side branch exacerbated these patterns and gave rise to a reversing flow region downstream of the ostium. Incorporation of more realistic geometric features had only minor effects and patterns of mean WSS under pulsatile conditions were similar to the steady flow results. Aspects of the observed WSS patterns correlate with, and may explain, some but not all of the lesion patterns in human, rabbit and mouse aortas.