We present a new microscopic model of growth and sublimation (g/s) of ice crystals in the atmosphere. This model is based on the assumption that the flux of vapor to the crystal surface is uniform over each flat crystal face. It thus differs fundamentally from the standard ''capacitance'' model for crystal growth, in which the mixing ratio is assumed uniform at the surface. In the new model the surface influence on growth is calculated self-consistently in terms of local environmental conditions, again differing sharply from the standard models in which this influence is either ignored or assigned a uniform, externally prescribed value. The new model leads to predictions of the evolution of ice crystal shape as well as mass. We find that predicted g/s rates are generally smaller than those predicted by the earlier models. The general trends both in g/s rates and in crystal hollowing predicted by the model are consistent with field and laboratory observations. The values of certain surface parameters needed for application of our model must be found from experiment. We review and compare the relevant laboratory experiments on ice crystal g/s rates and show their lack of mutual consistency. Therefore the surface parameters inferred from these experiments are necessarily uncertain. We show that the surface parameter values can be inferred from observations of crystal hollowing, since our model allows the prediction of environmental conditions at which hollowing should occur. ¿ American Geophysical Union 1996