The aim of this research is to present a novel 3D simulation procedure to assess microwave induced stresses in inhomogeneous hard rocks at a microstructure level. For a realistic rock model a two-component 3D microstructure is generated by a Voronoi tessellation algorithm. The two components are microwave absorbing (phase A) and transparent (phase T), respectively. In order to calculate the electric field inside the inhomogeneous rock, a 3D finite difference time domain (FDTD) simulation is performed. The absorbed heat is computed and applied as temperature distribution in a subsequent thermo-mechanical finite element (FE) analysis in order to calculate the thermally induced stresses. Two irradiation times (15 s and 25 s) and a microwave power of 25 kW at 2.45 GHz as well as three different morphologies are analyzed. Moreover, the phase transformation of quartz at 573 degrees C is considered in the FE model. The influence of the anisotropic nature of the quartz grains is assessed by comparing the stress formation in the isotropic with those of the anisotropic case. A comparative analysis with a homogeneous model is performed in order to draw conclusions on the influence of the microstructure on the microwave induced stress formation. High maximum principal stresses on the boundaries of the microwave absorbing phase (phase A) exceeding the tensile strength are observed in the 15 s irradiation model. After 25 s of microwave irradiation even higher stresses as a consequence of phase transformation of quartz are determined. In the anisotropic case significantly more areas with high maximum principal stresses especially in phase T are observed. Microwave irradiation experiments on granite samples are performed in order to correlate the numerical results with experiments. (C) 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).