Brittle ceramics that inherently contain micro-structural defects often suffer from catastrophic failure. Combining materials with different thermal expansions in a multi-layered composite to purposefully induce residual stresses is a promising strategy for increasing the resistance to crack initiation. A layer with compressive residual stress may improve the apparent strength by counterbalancing the tensile applied load. This strategy always comes at the cost of introducing tensile residual stresses in other locations that may become critical locations for forming cracks. This work aims to develop computational models based on finite fracture mechanics for predicting the formation of cracks in multi-layered ceramic composites under different loading scenarios. Finite element models of common loading scenarios were implemented, such as a build-up of residual stresses during cooling from sintering, thermal shock, and contact of ceramic with a hard ball. Crack formation governed by a coupled stress-energy criterion was simulated in these models. The volume ratio of the combined material determines the residual stresses, which, in tandem with the thicknesses of the layers, significantly impact the crack formation. Alumina, zirconia, and their mixture were selected as representative materials for which the size effect of layer thickness was demonstrated. Parametric analyses were performed for various combinations of layer thickness and residual stresses to determine the limitations of laminate architectures able to withstand residual stresses and rapidly changing stresses during a thermal shock. Other parametric analyses were performed for plate indentation by hard balls, which exhibit a size effect with the changing diameter of the indenter ball. The coupled criterion approach yielded experimentally verified fracture predictions. Additionally, it provided insight into the mechanisms of crack formation, explaining, for instance, the observed position of cracks outside the most stressed regions. Different sensitivities to the values of the fracture toughness and the tensile strength were revealed in various loading scenarios.