The mobility of charge carriers in silicon can be significantly increased when silicon is subject to a field of strain. In a microelectronic device, however, the strain field may be intensified at a sharp feature, such as an edge or a corner, injecting dislocations into silicon and ultimately failing the device. The strain field at an edge is singular, and is often a linear superposition of two modes of different exponents.The relative contribution of the two modes is characterized by a mode angle, and the critical slip systems are determined as the amplitude of the load increases. Critical residual stress is calculated in a thin-film stripe bonded on a silicon substrate for different geometries and material conditions. In particular, the effect of elastic mismatch between island and substrate is studied, yielding a profound understanding of the importance of the two modes describing the singular stress field.