Brownian dynamics simulations of hyperbranched polymers with different degrees of branching have been performed under the influence of simple shear flow. Hydrodynamic and excluded-volume interactions have been taken into account explicitly. Shear-thinning effects have been observed for all simulated degrees of branching. As the molecular weight of highly branched structures increases, the zero shear rate intrinsic viscosity reaches a maximum and begins to fall similar to the intrinsic viscosity behavior of perfectly branched dendrimers. In the absence of shear, static structure factors, S(k), for hyperbranched polymers with the smallest number of monomers studied resemble those of a three-arm star. As the number of monomers increases and as the degree of branching increases, the S(k) curves for the hyperbranched polymers begin to illustrate features associated with S(k) curves for hard spheres. Further insight into the shape and interior density of these structures is obtained through the ratio of the radius of gyration, R-g,, to the hydrodynamic radius, Rh. The ratio R-g/R-h is observed to approach unity as the number of monomers and the degree of branching increase.