Solutions are provided for the two-dimensional diffusion equation of dust over a rough ground surface under the effect of horizontal wind and gravitational attraction. A general analytic expression for the two-dimensional dust concentration is obtained. It is shown that the one-dimensional result derived previously for the vertical transport of dust can easily be deduced as a special case of this expression. The profiles of the concentration above the roughness height are evaluated numerically and are found to depend strongly on downwind positions. The numerical values of the concentration at a particular downwind position are found to be smaller than those predicted by the one-dimensional theory. (author). 3 refs, 9 figs, 1 tab.