A new porous media mathematical model for freeze-drying was developed based on the adsorption-desorption relationship proposed in this paper. A finite difference solution was obtained from a moving boundary problem for the dielectric-material-assisted microwave freeze-drying process. Silicon carbide (SiC) was selected as the dielectric material; and frozen skim milk was used as the aqueous solution to be dried. Simulation results showed that the dielectric material can significantly enhance the microwave freeze-drying process. The drying time was 33.1 % shorter than that of ordinary microwave freeze-drying under typical operating conditions. When the solid content of the solution to be freeze-dried was very low, or the solid product had a very small loss factor, microwave heating was less effective without the assistance of dielectric material. The mechanisms of heat and mass transfer during drying were analyzed based on profiles of ice saturation, temperature and vapor concentration. Drying rate-controlling factors were discussed. A comparison was made between the model predictions and the reported experimental data. (c) 2005 Elsevier Ltd. All rights reserved.