Modern power semiconductor devices used in automotive products and industrial systems have to reliably withstand up to 10^9 and more high power density electrical pulses. The heat generated during the electrical power pulses (active cycling) results in temperature fluctuations leading to thermally-induced cyclic stresses in the metallization stack of power semiconductors which may cause material degradation and device failure. The present work aims to develop a simulation methodology for modeling damage behavior in the metallization stack of power semiconductors subjected to active thermal cycling. The developed methodology is applied in Finite Element Method simulation studies to improve the understanding of the degradation behavior in the chip metallization under such loading conditions. The work focuses on the description of fatigue failure in the power metallization stack. The problem at hand is dealt with by utilizing two complementary approaches. First, to predict the locations of fatigue crack formation when these are not known a priori, the simulation methodology employs fatigue indicator parameters based on multiaxial fatigue models. By application of the critical plane based fatigue indicators, the orientation of the crack plane during the early crack growth can be predicted as well. To this end, the procedure for computation of the critical plane based fatigue indicators is implemented in an in-house parallel software code. The predicted crack nucleation sites and directions of the early growth in the power metallization layer under active cycling conditions are compared with experimentally observed cracks in the power-Cu layer of a power semiconductor device. Second, fatigue crack growth under active cycling conditions is simulated using the cohesive zone modeling concept within the framework of the Finite Element Method. To this end, a cyclic cohesive zone model based on a damage evolution equation is extended onto the case of transient thermal loading conditions and is implemented into a commercially available Finite Element simulation code. The thermal and mechanical interaction of the cohesive surfaces is taken into account for both open and closed crack states. By incorporating the temperature dependence of the cohesive zone model parameters, the model is also extended onto cases of nonisothermal fatigue. To speed-up fatigue simulations, the cyclic cohesive zone model is equipped with the cycle jump technique based on direct iteration of the damage evolution equation. The implemented thermomechanical cyclic cohesive zone model is applied to a problem of interfacial debonding between two layers of a power metallization stack subjected to the active thermal cycling. The numerical simulation of crack growth in microelectronic devices under active cycling conditions is a computationally intensive task. To obtain computationally efficient Finite Element Models while preserving high spatial resolution in the regions of cracking, the model size reduction is performed based on the submodeling technique. The obtained detailed temperature, stress and strain fields are analyzed by the developed methodologies with respect to the fatigue behavior of the power metallization layer. The evolution of cyclic stress and cyclic plastic strains including the effect of residual stresses is considered.