This paper is the first in a three part series describing numerical simulations of hailstorms and hailstone growth using a two-dimensional, time-dependent cloud model. In this model. cloud water, cloud ice and rain are treated via standard parameterization technique The precipitating ice field is discretized into 20 logarith-mically spaced size categories which evolve in, and interact with the time-dependent dynamic framework. Ice particles are generated by the freezing of raindrops and via a parameterization of the Bergeron process. Growth of these ice particles is based on wet and dry growth concepts applied to the continuous accretion process. The model has been used to simulate a severe supercellular hailstorm from the National Hail Research Experiment These simulations include cases assuming various microphysical configurations of the model along with simplified cloud seeding experiments The simulations indicate many areas of agreement between the model results and observation chief among them being the characteristic sloping updraft and moving gust front, the rounded dome cloud top, the radar overhang, and the intense precipitation cascade. The major observed features which were not properly simulated were the persistent bounded weak echo region and the high concentrations of giant hail and associated high radar reflectivity values. The model results have also been compared to and are consistent with aircraft measurements of the thermodynamic structure of the subcloud region, and the basic internal structure of hailstorms. The model simulations and the storm were prodigious producers of surface rain and hail. The model was unable to simulate the vast amounts of large hail observed for this case, mainly due to depiction of the cloud water caused by embryo generation mechanisms being too efficient, although the two-dimensionality of the model may also limit hail production. Recirculation of hall embryos from the forward overhang back down into the leading edge of the sloping updraft was important to hail production according to both the observations and the model results. The overall effect of the cloud seeding, although dependent on the magnitude and duration of the seeding, was quite similar in all cases. The primary seeding, effect was the creation of more small ice particles, most of which were carried aloft into the anvil. Dynamic effects induced by the seeding were generally insignificant. In all seeded cases the amount of hail at the surface was reduced, although the undesirable response of decreased rainfall also resulted.