We study the problem of heating a one-dimensional approximation to a slab-sided moist foodstuff in a microwave oven, allowing for a phase change and drying. We initially investigate the accuracy of the Lambert law of exponential decay of the applied electric field into the foodstuff and derive an approximation for the field comprising the exponential decay term and an oscillatory component. We then show that the temperature of the foodstuff is given, to a good approximation, by only considering the heating effects of the exponentially decaying field. We then study the effects of drying. This process changes the dielectric properties of the material, which leads to changes in the field. However, these lead to smaller changes in the moisture content. A fast and accurate numerical method is derived which relies on smoothing the phase transition. (C) 2010 Elsevier Ltd. All rights reserved.