An analytical model describing the combined effect of mass accomodation and net adsorption of trace gases on the surfaces of growing ice particles (trapping) is developed. An approximate solution for the release of trapped trace gases from evaporating ice particles is also given. The model fully accounts for the fact that atmospheric ice particles frequently experience substantial subsaturations and supersaturations. In such situations, pure adsorption models cannot be employed to calculate the trace gas uptake. Limiting cases are discussed in which uptake is solely controlled by gas diffusion (burial limit) or by surface kinetics (adsorption limit). The model results are expressed in terms of a nonreactive uptake coefficient for use in atmospheric models. Crucial factors controlling trapping are the rate of desorption (or net molecular escape rate) and the ice growth rate. Trace gase molecules can be effectively trapped in bulk ice even at low ice supersaturations when their times of adsorption are sufficiently long. The trapping model may help provide physically sound interpretations of field and laboratory measurements of trace gas uptake on growing ice surfaces. Previous global model studies of nitric acid uptake in cirrus clouds only considering adsorption likely underestimated the resulting dentrification, because the vertical redistribution is driven by the largest ice crystals which trap nitric acid most efficiently.