Two semiempirical models of generalized Newtonian fluid are discussed. Special attention was focused on the stress dependent model based on the free volume theory. However, the strain-rate dependent model in form of a modified viscosity function resulting from Oldroyd equation is also presented. Both models (along with specific cases) reflecting pseudoplastic or dilatant behavior of liquids in shear flows are generalized to multimode models (defined as products of two or more basic models), which are able to describe quantitatively the behavior of more complex systems, for example, systems with pseudoplastic and dilatant properties in different shear stress (shear rate) ranges. A number of practical examples for viscosity curves of non-Newtonian fluids described by these models are given. The questions of inverse models and model efficiency are also discussed. POLYM. ENG. SCI., 58:1446-1455, 2018. (c) 2017 Society of Plastics Engineers