A Brownian dynamics algorithm is developed to simulate dynamics experiments of rigid macromolecules. It is applied to polarized dynamic light scattering from rodlike sturctures and from a model of a DNA fragment (762 base pairs). A number of rod cases are examined in which the translational anisotropy is increased form zero to a large value. Simulated first cumulants as well as amplitudes and lifetimes of the dynamic form factor are compared with predictions of analytic theories and found to be in very good agreement with them. For DNA fragments 762 base pairs in length or longer, translational anisotropy does not contribute significantly to dynamic light scattering. In a comparison of rigid and flexible simulations on semistiff models of this fragment, it is shown directly that flexing contributes to the faster decay processes probed by light scattering and that the flexible model studies are in good agreement with experiment.