A numerical model for the computation of tephra fall accumulation resulting from Plinian or sub-Plinian eruptions is presented. Mass accumulation at the ground level is found by solving a continuity equation which describes the transport of tephra in the atmosphere. The treatment incorporates horizontal advection due to wind, vertical gravitational settling, and dispersion due to atmospheric turbulence. Aspects of the parameters which enter the model, such as settling velocity, diffusion coefficients, deposition velocity, and source shape, are considered and discussed. Particular attention is devoted to settling velocity dependence on particle size and density, to deposition velocity behavior in weak and strong wind fields, and to eddy diffusion coefficient dependence on atmospheric conditions, particle size, and density. The results for some theoretical cases are presented to illustrate the behavior of the model. The validity of the model is tested by comparing observed and calculated deposits for the May 1980 Mount St. Helens eruption. The model predicts a double thickness maximum, the first near the volcano, the second at a distance of about 300 km, as was observed in the actual deposit. ¿ American Geophysical Union 1988