A comprehensive 3D simulation research of the stress formation on the microstructure level of hard rocks due to microwave irradiation applied in microwave assisted rock breakage is presented. The specific aim of the present work is to investigate the influence of microstructural details in inhomogeneous rocks. In order to use a realistic rock model, a two component 3D microstructure is generated. The two components are microwave absorbing and transparent, respectively. In the first step of the simulation chain the electric field inside the inhomogeneous rock is obtained by a 3D finite difference time domain (FDTD) calculation. In a subsequent thermo-mechanical finite element (FE) simulation the stresses generated by 15 s heating with 25 kW are obtained. High stresses on the boundaries of the microwave absorbing phase exceeding the tensile strength are observed. Finally, the numerical results are corroborated by microwave experiments performed on granite samples.