<p>Bile has been shown to be a non-Newtonian fluid. This viscoelastic fluid exhibits both shear thinning and strain hardening properties. It is important to consider the strain hardening properties when studying bile flow because it is related to the viscosity of bile in the bile ducts. The second and third invariants of the flow equation regulating generalized Newtonian and viscoelastic fluids were discussed in this study. A viscosity model combining shear thinning and strain hardening behaviors of bile was proposed in this study. The bile flow through an idealized three-dimensional cystic duct was simulated with this combined viscosity model, and the results showed that the extensional characteristics of bile enhance the viscosity and resistance to the flow of bile, especially near the spiral valve Heister. The non-Newtonian properties of bile have a significant impact on the resistance of the flow. As a result, the pressure drop in the cystic duct was increased when the strain hardening property was added to the viscosity model of the bile.</p>