A finite difference quasi-static thermo-mechanical 2-D model of a theoretical 2-phase mineral is constructed. The aim is to simulate the thermal stresses generated and subsequent thermal damage when a rock particle is exposed to high electric field strength microwave energy. The influences of power density and grain size are assessed for a theoretical 2 mm by 2 mm sample of calcite host rock deemed transparent to microwave energy, containing a strongly absorbent circular pyrite phase of varying diameter. The simulations have predicted the extent of microwave heating, thermal conduction and expansion, strain softening and thermally induced fracturing. The stress regime is analysed and it is concluded that fractures are likely to occur around the grain boundary between absorbent and transparent species. This suggests that liberation of valuable minerals can be improved and that a reduction in comminution energy is possible after microwave treatment. The effect of size on peak temperatures is analysed, and it is shown why microwave treatment is less efficient at lower particle sizes for a fixed applied power density. (c) 2004 Elsevier Ltd. All rights reserved.