It is known that rock fracture includes inelastic straining or damage that should localize at a certain loading stage and result in fracture initiation. The details of this process are not clear, and it is frequently omitted in the models by imposing the initial microcracks (seeds) with certain lengths and orientations. Here we investigate 2-D systems of three layers in finite-difference models. The layers subjected to the horizontal extension are separated by cohesive-frictional interfaces and have contrasted properties typical of sedimentary piles. Fractures are initiated in a more brittle central layer in the vicinity of the interfaces with the adjacent layers. It starts with the initially distributed inelastic straining, which then localizes into narrow bands. The damage within these bands is strongly accelerated, resulting in complete material failure locally. Short initial fractures corresponding to narrow bands of failed material are normal to the least local stress. They then propagate from the interfaces to the layer center with further extension. We carefully investigate the impact of different regularization procedures, the grid geometry, and structure on all stages of the fracture process and define the optimal conditions that can be applied for fracture modeling in different structural and loading configurations.