Dendrimers are a relatively new class of highly branched polymers consisting of short chain units with multifunctional groups at both ends. Starting from an initiator core, the successive reaction of the functional groups with other units generates a highly branched molecule which resembles a Cayley tree [1,2]. Theoretical work on dendrimers has focused largely on determining the structure of isolated homogeneous dendrimers. Numerical selfconsistent mean-field calculations have also been performed for individual dendrimers. Some molecular simulation studies have been reported to determine the structure of isolated  and bulk  homogeneous dendritic polymers; however, the focus of these simulation studies has been exclusively equilibrium properties. The unique nature of dendrimers means that significant differences could be reasonably expected in their transport properties compared with other polymers of similar size. In this work, we use non-equilibrium molecular dynamics (NEMD) [5,6] to investigate the behavior of dendrimers under shear. The shear viscosity, energy and pressure are reported for generation up to 4 using both constrained bonds and FENE bonds. NEMD results are also presented for linear polymers of similar molecular weight. The results indicate dendrimers behave differently with respect to the onset of non-Newtonian behavior compared with linear polymers. 1. Tomalia, D. A., Baker, H., Dewald, J. R., Hall, M., Kallos, G., Martin, S., Roeck, J., Ryder, J., and Smith, P. Macromolecules 19, 2466 (1986). 2. Voit, B. I. Acta Polym. 46, 87 (1985). 3. Naylor, A. M., Goddard, III, W. A., Kiefer, G. E. and Tomalia, D. J. Am. Chem. Soc. 111, 2339 (1989); Mansfield, M. L. and Klushin, L. I. Macromolecules 26, 4262 (1993); Murat, M. and Grest, G. S. Macromolecules 29, 1278 (1996); Chen, Z. Y. and Gui, S.-M. Macromolecules 29, 7943 (1996); Lue, L. and Prausnitz, J. M. Macromolecules 30, 6650 (1997). 4. Lue, L. Macromolecules 33, 2266 (2000). 5. Evans, D. J. and Morriss, G. P., Statistical mechanics of Nonequilibrium Liquids, Academic Press, London, 1990. 6. Sadus, R. J., Molecular Simulation of Fluids: Theory, Algorithms and Object-Orientation, Elsevier, Amsterdam, 1999.