The alternating flow model (AFM) views dispersion in packed beds as a sequence of streamline plugs that must repeatedly split and merge as the bulk fluid traverses the vessel. Thus, the flow in the AFM is ordered, as opposed to the random flow implied by the Fickian analogy. For mass dispersion only, model parameters arise from a priori considerations of packing geometry. Steady state and transient data (5.6 < Dt/dp < 54.4, 100 < Rep < 1,000, gases and liquids) show the AFM to surpass the Fickian analogy (based on correlations for dispersion coefficients) in most cases. Further, it can describe well the radial velocity profile trends in packed beds. For heat dispersion, two additional parameters (heat transfer coefficients) arise that are not functions of packing geometry. Simple correlations for these parameters and the justifications are given. Most of the comparisons made with the literature experimental results show the AFM to be at least as good as the back-fit Fickian analogy. The AFM should be most useful for packed beds with a relatively small Dt/dp.