A singular stress field can occur at the edge of the joint plane in a thermally or mechanically loaded material compound. This stress field was calculated analytically and was compared with the results from the finite element method. If one of the two partners consists of ceramic material, unstable crack spread starting from faults in this strongly stressed area can lead to failure. In linear elastic material, the behaviour of a crack is clearly described by the stress intensity factors. These can be calculated for a known stress distribution in the uncracked structure by the method of the weight function. The corresponding weight functions for surface cracks parallel to the boundary surface were determined with the aid of suitable reference load cases. The effect of the position of the crack in the compound and the elastic constants of the compound are discussed. For examples, the stress intensity factors for cracks in a thermally stressed material compound were determined by the ...