Blood flow temporal waveforms change with position along an artery. The change in the flow waveforms can be accounted for by a transmission line model of flow. According to this model, pulse waves propagate at a finite velocity in both directions along the artery. In principle, given flow waveforms measured at three locations along an artery, the pulse-wave velocity, (c) can be determined from the wave equation ( equals , Q is flow, t is time, z is position). Given the vessel diameter, the vessel-wall compliance can be derived from pulse-wave velocity. However, direct solution of the wave equation for pulse-wave velocity is highly susceptible to flow-measurement error. Thus, we propose a new method for estimating pulse-wave velocity from arterial flow waveforms. In our method, ideal flow waveforms are reconstructed from three measured flow waveforms. The ideal waveforms are reconstructed by minimization of the total error between the ideal and measured waveforms subject to constraints of the wave equation. Ideal flow waveforms are reconstructed for a range of assumed pulse-wave velocities. The true pulse-wave velocity is considered to be that which produces the minimum total error. The method applied to blood flow measurements made with phase-contrast magnetic resonance imaging.