This thesis aims to efficiently predict crack initiation from pores using the combined criterion. The pores are created out of computed tomography (CT) images. The combined criterion states that a crack initiates when both the stress criterion and the energy criterion are fulfilled. According to the stress criterion, the stress up to the crack initiation position must be greater than a critical stress. According to the energy criterion, the energy release rate at the crack initiation position must be at least as great as the critical energy release rate of the material. A multi-scale approach is used to predict crack initiation and consists of a component model, a local model with one pore, and a crack model. The component model determines the strain tensor, which is applied as a load on the local model with periodic boundary conditions. The local model contains the pore from the CT image. The "Marching Cubes" algorithm extracts the pore surface from the CT image. The local model is simulated with FEM. The results of the FEM simulation and the curvatures of the extracted pore surface are transferred to the crack model, which determines the largest principal stresses and the energy release rates. The largest principal stresses and the energy release rates can be obtained by FEM simulations, but this is too time-consuming. So instead of FEM simulations, a statistical model based on more than 98000 in advance simulated FEM computations predicts the greatest principal stresses and the energy release rates. The combined criterion predicts a failure index out of the material parameters, the predicted greatest principal stresses, and the predicted energy release rates. If the failure index is less than one, no crack initiation is predicted, otherwise a crack initiates under the applied load according to the criterion. In an example, the predicted failure index deviates by 15% from a failure index computed with submodels.