Mechanical comminution of rocks is an energy intensive process with energy efficiency around 1%. A possible way to enhance the efficiency is the prior application of high-power microwaves. Microwave irradiation of a heterogeneous material introduces inhomogeneous electromagnetic and thermal fields which result in stresses and potentially in damage. In order to assess the industrial applicability, various 3D numerical analyses with either constant microwave power or constant energy were performed on granite samples. To this end dielectric and thermal properties were taken from measurements. For the numerical computations a realistic 3D microstructure was generated by a Voronoi tessellation algorithm. In order to calculate the electromagnetic field inside the rock sample, a finite difference time domain simulation was performed. The resulting temperature as well as stress field is evaluated in finite element analyses. The numerical results were corroborated by microwave irradiation experiments on granite samples.