The circulatory systems of vertebrate animals are closed, and blood leaves and returns to the heart at the same level. It is often concluded, therefore, that the heart works only against the viscous resistance of the system, not against gravity, even in vascular loops above the heart in which the siphon principle operates. However, we argue that the siphon principle does not assist blood flow in superior vascular loops if any of the descending vasculature is collapsible. If central arterial blood pressure is insufficient to support a blood column between the heart and the head, blood flow ceases because of vascular collapse. Furthermore, the siphon principle does not assist the heart even when a continuous stream of blood is flowing in a superior loop. The potential energy gained by blood as it is pumped to the head is lost to friction in partially collapsed descending vessels and thus is not regained. Application of the Poiseuille equation to flow in collapsible vessels is limited; resistance depends on flow rate in partially collapsed vessels with no transmural pressure difference, but flow rate is independent of resistance. Thus the pressure developed by the heart to establish a given flow rate is independent of the resistance occurring in the partially collapsed vessels. The pressure depends only on the height of the blood column and the resistance in the noncollapsed parts of the system. Simple laboratory models, involving water flow in collapsible tubing, dispel the idea that the siphon principle facilitates blood flow and suggest that previously published results may have been affected by experimental artifact.