Alignment of arterial endothelial cells with the mean wall shear stress (WSS) vector is the prototypical example of their responsiveness to flow. However, evidence for this behaviour rests on experiments where many WSS metrics had the same orientation or where they were incompletely characterised. In the present study, we tested the phenomenon more rigorously. Aortic endothelial cells were cultured in cylindrical wells on the platform of an orbital shaker. In this system, orientation would differ depending on the WSS metric to which the cells aligned. Variation in flow features and hence in possible orientations was further enhanced by altering the viscosity of the medium. Orientation of endothelial nuclei was compared to WSS characteristics obtained by computational fluid dynamics. At low mean WSS magnitudes, endothelial cells aligned with the modal WSS vector whilst at high mean WSS magnitudes they aligned so as to minimise the shear acting across their long axis (“transverse WSS”). Their failure to align with the mean WSS vector implies that other aspects of endothelial behaviour attributed to this metric require re-examination. The evolution of a mechanism for minimising transverse WSS is consistent with it having detrimental effects on the cells and with its putative role in atherogenesis.