Nonequilibrium molecular dynamics simulations have been performed on model fluids representing eicosane isomers in order to investigate the effect of branching and side chain position on fluid rheology. A heterogeneous, united-atom model with 20 Lennard-Jones interaction sites located at carbon centers was used to model the fluids. Vibrations and bond rotations were frozen, but torsional rotation was included. It was found that viscosity increases significantly from the n-alkane structure to a branch on carbon 2, but the movement of the branch along the carbon backbone has a smaller increasing than decreasing effect. The size of the group in a branched position has a more substantial effect upon the viscosity.