The veins distributing oxygenated blood from the placenta to the fetal body have been given much attention in clinical Doppler velocimetry studies, in particular the ductus venosus. The ductus venosus is embedded in the left liver lobe and connects the intra-abdominal portion of the umbilical vein (IUV) directly to the inferior vena cava, such that oxygenated blood can bypass the liver and flow directly to the fetal heart. In the current work, we have developed a mathematical model to assist the clinical assessment of volumetric flow rate at the inlet of the ductus venosus. With a robust estimate of the velocity profile shape coefficient (VC), the volumetric flow rate may be estimated as the product of the time-averaged cross-sectional area, the time-averaged cross-sectional maximum velocity and the VC. The time average quantities may be obtained from Doppler ultrasound measurements, whereas the VC may be estimated from numerical simulations. The mathematical model employs a 3D fluid structure interaction model of the bifurcation formed by the IUV, the ductus venosus and the left portal vein. Furthermore, the amniotic portion of the umbilical vein, the right liver lobe and the inferior vena cava were incorporated as lumped model boundary conditions for the fluid structure interaction model. A hyperelastic material is used to model the structural response of the vessel walls, based on recently available experimental data for the human IUV and ductus venous. A parametric study was constructed to investigate the VC at the ductus venosus inlet, based on a reference case for a human fetus at 36 weeks of gestation. The VC was found to be [Formula: see text] (Mean [Formula: see text] SD of parametric case study), which confirms previous studies in the literature on the VC at the ductus venosus inlet. Additionally, CFD simulations with rigid walls were performed on a subsection of the parametric case study, and only minor changes in the predicted VCs were observed compared to the FSI cases. In conclusion, the presented mathematical model is a promising tool for the assessment of ductus venosus Doppler velocimetry.