Numerical simulations of flow dynamics of milk using a volume-of-fluid (VOF) method were carried out to understand detailed fluid mechanics of milk in a process in which milk was filled into a gable-top carton with the volume of 1000 mL. All physical properties of milk were measured, and it was verified that in its rheological properties, milk was a purely viscous non-Newtonian fluid with shear-thinning property. In the numerical simulation, the shear-thinning property of milk was modeled with the Carreau-Yasuda model, in which the operating condition for the milk-filling process was set as the computational condition. The numerical results showed that the viscosity of milk was drastically changed in the milk-filling process and that a complicated viscosity profile was formed inside the carton. By comparing numerical results of milk with those of Newtonian fluids, the characteristics of the flow dynamics of milk were more visible. Consequently, it was revealed that the shear-thinning property of milk largely influenced fluid flows inside the carton. Hence, the shear-thinning property of milk cannot be ignored in milk-flow simulations. Numerical analysis will be a useful tool for understanding local changes in the shear-thinning viscosity.