This study is based on the hypothesis that the pressure within the arterial network can be usefully decomposed as the sum of a reservoir pressure and an excess pressure. The reservoir pressure waveform is defined to be the same in each vessel but delayed by the wave travel time from the root of the aorta. Using calculus of variations and mass conservation, which relates the flow and rates of change of pressure in the vessels, we show that the reservoir pressure waveform minimises the ventricular hydraulic work for any physiologically or clinically reasonable ejection waveform and arterial properties, i.e. vessel compliances and terminal resistances. We conclude that the excess pressure determines the excess work done by the ventricle, which may have clinically important implications.