A hemodynamic model for pulsatile fluid flow in a pressurized thin-walled elastic tube was applied for the computation of volumetric blood flow and velocity profiles for a given set of system parameters at any selected location along the umbilical artery. The velocity profiles over one heart cycle provide the fetal blood flow velocity waveforms (FVW) from which the usual Doppler indexes (DI) can be derived. The model was used for a comprehensive investigation of the correlation between DI and system parameters that reflect the anatomy and physiology of umbilical blood flow. The simulations showed that the radial location of the Doppler measurement is insignificant for the calculated DI, whereas the axial site is important. The analysis showed that decreasing the diameter or increasing the length of the umbilical artery reduces fetal mean blood flow rate and increases the DI. Increasing blood viscosity tends to induce similar patterns, whereas decreasing arterial compliance or increasing blood density decreases the DI with little effect on blood flow rate. Fetal heart rate has a minor effect on both DI and fetal blood flow rate. This study provides insight into the dependence of DI on the anatomic and physiological characteristics of umbilical blood flow.