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. The aim of this thesis is to determine the microwave induced stresses and damage in heterogeneous (e.g. granite) as well as homogeneous hard rocks (e.g. basalt). In the heterogeneous case a novel 3D simulation procedure to assess microwave induced stresses at a microstructure level is presented. For a realistic rock model two and three component 3D microstructures are generated by a Voronoi tessellation algorithm. In order to calculate the electromagnetic field inside the inhomogeneous rock, a 3D finite-difference time-domain (FDTD) simulation is performed. A microwave source with a typical technical frequency of 2.45 GHz is assumed. 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 and damage. With a 3D two component model the influence of the microstructure on the microwave induced stress formation during microwave irradiation with a 25 kW source for 15 s and 25 s is assessed. In the 25 s case the effect of the α to β phase transformation of quartz at 573°C is investigated. The influence of the anisotropic nature of the quartz grains is assessed by comparing the stresses in the isotropic with the anisotropic case. High maximum principal stresses on the boundaries of the strong microwave absorbing phase 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 a significantly higher fraction exhibiting high maximum principal stresses especially in the microwave transparent phase are observed. By considering a non-linear damage material model, damage initiation around the main heated area and at the phase boundaries of the strong absorbing phase are determined. These observations correlate qualitatively with microwave irradiation experiments. It is concluded that the formation of stress and damage is highly influenced by the microstructure and the micromechanical behavior of the constituents (quartz phase transformation, anisotropic behavior). In order to assess the industrial applicability, numerous 3D numerical analyses with varying irradiation times as well as microwave powers are performed on granite three component models. To this end measured dielectric and thermo-mechanical properties are used. Both constant microwave power and varying irradiation times as well as constant microwave energy and different irradiation time / power cases are investigated. Under constant power the largest maximum principal stresses rise linearly with the irradiation time whereas with constant energy an optimum irradiation time can be found giving maximum stresses. The presented 3D inhomogeneous simulation methodology allows to determine the optimum microwave irradiation parameters for the investigated granite.