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A completely coupled 3 dimensional model is developed for the microwave heating of porous high moisture biological materials. The model considers the interaction between the electromagnetic fields and the heat and mass transfer processes. The model takes into account the presence of multiple modes in the microwave oven. The variation of material properties on temperature is considered in the model. The model is solved numerically using finite differences for electromagnetic field and finite volume methods for heat and mass transfer process. It predicts the internal moisture movement, liquid expulsion by Darcy flow, and the highly uneven moisture and temperature profiles. The model developed is useful not only for heating of foods but also for heating of ceramics and other porous materials.