The author discusses the discretation and numerical solution of a large system of partial differential equations modeling the long range transport of air pollutants over large geographical areas (e.g. all of Europe) and long time periods (at least one year). The commonly used discretation scheme results in a very large system of ordinary differential equations (about 10 5 equations for the three (space) dimensional problems) which makes simulation studies intractable on sequential computers. Thus, successful utilization of the algorithm has been previously accomplished only for the two (space) dimensional problem. The author discusses how to vectorize appropriate parts of the algorithm in order to obtain a code which is numerically tractable for even three-dimensional problems (on CRAY type machines).