This article describes the modified arterial reservoir in detail. The modified arterial reservoir makes explicit the wave nature of both reservoir ( Pres) and excess pressure ( Pxs). The mathematical derivation and methods for estimating Pres in the absence of flow velocity data are described. There is also discussion of zero-flow pressure ( Pzf), the pressure at which flow through the circulation ceases; its relationship to asymptotic pressure ( P∞) estimated by the reservoir model; and the physiological interpretation of Pzf . A systematic review and meta-analysis provides evidence that Pzf differs from mean circulatory filling pressure.