A finite element numerical model is used to predict the thermal and mechanical response of mineral-bearing ores irradiated by microwave energy. The model considers a small, spherical, pyrite particle surrounded by a matrix of calcite. Power density data are determined from the dielectric properties of the mineral and host rock materials at typical microwave frequencies and power capabilities. The effects of varying power density and mineral particle diameter are studied. Using power densities within the expected achievable range for pyrite, significant temperature differences are predicted between the mineral particle and host rock. These temperature gradients lead to circumferential tensile stresses in the host rock well in excess of the reported uniaxial tensile strength of common rock materials. It is shown that, for a fixed microwave energy source, both the temperature difference between the mineral and host rock, and the peak tensile stress in the host rock are reduced as the mineral particle size is reduced. Recent experimental efforts to corroborate this numerical study are briefly described.