When the liquefied water-saturated sand is regarded as a fluid, it can be idealized as a kind of shear thinning non-Newtonian fluid. Based on non-Newtonian fluid mechanics, the theoretical analysis was conducted on the liquefied water-saturated sand. According to this, the relationship between the shear strain rate and the viscosity under zero effective stress state can be properly described by pure viscous flow constitutive model. The Gross model of liquefied water-saturated sand is established by fitting the flow curve of the dynamic torsional shear test results on the basis of predictions obtained from several commonly used pure viscous flow constitutive models. The representative model parameters include the relative density, the consolidation stress and the impact of stress history. The functional relationships among time dimension K, zero shear apparent viscosity η0 and limit shear apparent viscosity η∞ are fitted based on the dynamic torsional shear test results, and the physical meanings of the parameters are introduced in the composed function. The research landmarks a theoretical foundation for further analysis of large deformation of liquefied flows based on fluid mechanics theory.