A new theoretical model that was recently purposed for zero-shear viscosity has now been extended to the three-branch alkanes with pentyl, hexyl, or phenyl attachments. The model links the equilibrium theory of Simha-Somcynsky (SS) statistical thermodynamics of liquids and the transport theory of Eyring Significant Structure (ESS). The predicted quantity of hole fraction as a measure of the free volume, computed from the SS equation of state, plays a primary role in the theory to combine the both theories. The experimental PVTeta data from 310 to 408 K temperature and 0.1 to 344.5 MPa pressure range have been used. The proportionality constants of the activation energy and the transmission coefficient have been calculated for each species separately and they are in expected trend with the substituted ring structure. Satisfactory agreement in prediction of viscosity from the hole fraction has been obtained.