The calculation of the viscosity of 51 multicomponent (48 ternary and 3 quaternary) nonelectrolyte liquid systems has been performed by means of a model based on Eyring's theory of viscous flow and the UNIQUAC equation. More than 1000 viscosity data points, under 0.1 MPa and in the temperature range of 283.15-323.15 K, have been calculated. The model is based on pure-component viscosities, pure-component molar volumes, and pure-component size and shape parameters, as well as two interaction parameters per binary system. The model; binary interaction parameters were determined previously by correlation of experimental literature data on the viscosity of binary systems. A rather good agreement between experimental and calculated viscosities of ternary and quaternary liquid mixtures has been achieved. The overall mean relative standard deviation of the calculation is 2.95%. The results show that the model is adequate for estimating liquid mixture viscosities for different types of mixtures containing polar and nonpolar components.