A grey-box model, based on a priori knowledge about heat transfer with phase change and on microwave effects approached by a continuous function, is proposed to simulate the thawing of food in a microwave guide in fundamental TE1,0 mode. The partial differential equation describing heat transfer with phase change is reduced into a lumped parameters system using a 2D finite volumes scheme. The heating due to the microwaves is considered in the heat equation as the spatial variation of the microwave power flux. Flux variation is approached by a continuous function of temperature and of the wave power, whose coefficients are estimated via reverse techniques. Finally, the model is validated during the thawing of a block of tylose filling the section of the wave guide. (c) 2005 Elsevier Ltd. All rights reserved.