A molecular dynamics simulation study has been conducted in order to shed light on the effect of molecular shape and structure on the rheological properties of linear and branched polymer melts. Couette shear flow has been simulated using Lees-Edwards sliding bricks periodic boundary conditions. Bulk properties of linear, star, H-shaped, and comb-shaped molecules have been calculated for many isomers of C100H202 polyethylene melt in order to do a controlled study on the effects of molecular architecture. Generally, branched polymers such as star, H, and comb-shaped molecules in non-Newtonian regime exhibit larger shear viscosities at high shear rates than their linear counterparts with. the same molecular weight. However, the normal stress differences observed are higher for linear polymers. It is shown that while the shape of a molecule affects its rheological response, two important parameters, the effective length of the molecule and its degree of branching, ultimately dictate its response.