The flow pulsatility index, the ratio of flow pulse amplitude to mean flow over the cardiac cycle, has been used to quantify pulsatility of blood flow in the umbilical artery. In experiments with fetal sheep, we showed that the flow pulsatility index in the umbilical artery is accurately estimated by the ratio of total umbilico-placental vascular resistance (mean arterial pressure divided by mean umbilical flow) divided by fundamental impedance (umbilical vascular impedance at the heart rate frequency) times the pulsatility index (pulse/mean) of the arterial pressure that drives flow through this bed. The pulsatility index of arterial pressure is primarily determined by upstream factors (e.g. heart rate) whereas fundamental impedance depends primarily on the radius and viscoelastic wall properties of the umbilical artery. An increase in resistance in the microcirculation and/or veins causes proportional changes in the flow pulsatility index because these sites have little influence on fundamental impedance. However, an increase in resistance in the highly vasoactive umbilical arteries has offsetting effects on impedance and resistance; consequently, flow pulsatility changes little even when arterial vasoconstriction markedly reduces mean flow. We conclude that when arterial pressure pulsatility is stable, a change in the flow pulsatility index provides a useful indication of a change in resistance in the microcirculation and/or veins but will not reliably detect a resistance change in the artery.