A system of shallow-fluid equations on the rotating earth is integrated numerically as an initial and boundary value problem for air flow across a mountain barrier. The fluid is confined in a channel bounded by two parallel walls at 30N and 70S. The (idealized) Andes Mountains considered here are 4.75 km high and about 200 km wide on their western slope. A variable map factor in the east-west direction is applied so that the model permits increased resolution near steep topographic features. The scheme is found to be quite stable. The result is compared with a case where the mountains are smoothed and an equidistant grid is applied. Brief descriptions of dissimilarity between westerly and easterly flows across the barrier and the two-dimensional cascade process are also given.