This paper presents numerical simulations of the response of a biological cell during freezing. The cell is modeled as an aqueous salt solution surrounded by a semi-permeable membrane. The concentration and temperature fields both inside and outside a single cell are computed taking into account heat transfer, mass diffusion, membrane transport, and evolution of the solidification front. The external ice front is computed for both stable and unstable growth modes. It is shown that for the particular geometry chosen in this study, the instabilities on the front and the diffusional transport have only modest effects on the cell response. For the cooling conditions, solute and cell property parameters used, the low Peclet regime applies. The computational results are therefore validated against the conventional membrane-limited transport (Mazur) model. Good agreement of the simulation results with the Mazur model are obtained for a wide range of cooling rates and membrane permeabilities. A spatially non-isothermal situation is also considered and shown to yield significant differences in the cell response in comparison to the isothermal case. (C) 2003 Elsevier Ltd. All rights reserved.