The objective of the study is to investigate numerically the fluid‐structure interactions (FSI) in a patient‐specific arteriovenous fistula (AVF) and analyze the degree of complexity that such a numerical simulation requires to provide clinically relevant information. The reference FSI simulation takes into account the non‐Newtonian behavior of blood, as well as the variation in mechanical properties of the vascular walls along the AVF. We have explored whether less comprehensive versions of the simulation could still provide relevant results. The non‐Newtonian blood model is necessary to predict the hemodynamics in the AVF because of the predominance of low shear rates in the vein. An uncoupled fluid simulation provides informative qualitative maps of the hemodynamic conditions in the AVF; quantitatively, the hemodynamic parameters are accurate within 20% maximum. Conversely, an uncoupled structural simulation with non‐uniform wall properties along the vasculature provides the accurate distribution of internal wall stresses, but only at one instant of time within the cardiac cycle. The FSI simulation advantageously provides the time‐evolution of both the hemodynamic and structural stresses. However, the higher computational cost renders a clinical use still difficult in routine. Copyright © 2013 John Wiley & Sons, Ltd.