We present a novel analysis of arterial pulse wave propagation that combines traditional wave intensity analysis with identification of Windkessel pressures to account for the effect on the pressure waveform of peripheral wave reflections. Using haemodynamic data measured in vivo in the rabbit or generated numerically in models of human compliant vessels, we show that traditional wave intensity analysis identifies the timing, direction and magnitude of the predominant waves that shape aortic pressure and flow waveforms in systole, but fails to identify the effect of peripheral reflections. These reflections persist for several cardiac cycles and make up most of the pressure waveform, especially in diastole and early systole. Ignoring peripheral reflections leads to an erroneous indication of a reflection‐free period in early systole and additional error in the estimates of (i) pulse wave velocity at the ascending aorta given by the PU–loop method (9.5% error) and (ii) transit time to a dominant reflection site calculated from the wave intensity profile (27% error). These errors decreased to 1.3% and 10%, respectively, when accounting for peripheral reflections. Using our new analysis, we investigate the effect of vessel compliance and peripheral resistance on wave intensity, peripheral reflections and reflections originating in previous cardiac cycles. © 2013 The Authors. International Journal for Numerical Methods in Biomedical Engineering published by John Wiley & Sons, Ltd.