A two-dimensional model has been integrated for two years to study the evolution of the El Chichón aerosol cloud in the stratosphere, starting about three months after the eruption. Initial conditions for the backscattering ratios are taken from airborne lidar measurements, while observations taken at Mauna Loa are used to estimate the initial size distribution for the aerosols. Aerosols have been treated as a passive tracer, because the small changes in the stratospheric dynamics due to the aerosol interaction with solar and longwave radiation can only induce marginal effects on large scale transport. We have also completely neglected microphysical processes like coagulation as well as photochemical effects on chemically reacting species. Results are shown for aerosol extinction mixing ratios, optical thickness, mass column density and size distribution. Extensive comparison with available lidar measurements are also presented and discussed. Major discrepancies are noted between the measured optical thickness and the one predicted by the model with the former being systematically higher. Neglect of coagulation and nucleation prevents formation of large particles at high altitude which are depleted in the simulation by sedimentation. The interhemispheric asymmetry is overestimated by the model with much more aerosol being transported in the Northern Hemisphere than in the Southern Hemisphere. Other differences are found in the sudden changes in the aerosol distribution. It is argued that two dimensional models are not suitable to simulate sporadic events and that microphysics should be taken into account even several months after the eruption.