A two-dimensional axisymmetric, unsteady state model was developed to simulate the coupled heat and mass transfer process that occurs during the sublimation of pure ice from within vials in a laboratory-scale lyophiliser. The theoretical model was solved numerically using an explicit finite difference method. The modified Enter method was used to discretise in time and an adaptive time step strategy was employed to ensure stability. Novel features of the model described here include a consideration of the varying, pressure dependent, insulating effect of the air gap under the curved base of a typical lyophilisation vial and the determination of the effects of radiative heating. The theoretical model was capable of predicting and describing the observed motion of the ice sublimation front, the ice temperature profile, the drying time and the influence of the total pressure. The model also gave a theoretical prediction of the improvement in drying rate that might be achieved by adding an extra energy source. The work provides insights into the understanding of the beat and mass transfer process during the primary drying stage of lyophilisation that can be applied to the optimisation of freeze-drying cycle design. (C) 2004 Elsevier Ltd. All rights reserved.