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The construction of semiconductor devices, as well as other electron devices, often requires the utilization of brittle materials, such as the semiconductor itself, as part of a larger structure. Thermal stress, caused by cooling from high temperature bonding operations, can cause fracture of the brittle part, due to thermal expansivity mismatch with other parts of the structure. This paper considers a widely used type of bond, consisting of a nonpenetrating butt-joint, wherein the parts develop thermal stresses by reason of shear constraint in a solder layer. This type of joint is therefore called a shear-constrained bond. A one-dimensional, elastic analytical model is presented, which predicts the location and orientation of the principal tensile stress in a shear-constrained brittle strip. The tensile stress required for brittle fracture is shown to be induced, primarily, by shear tractions in the solder layer which are applied to one face of the strip. Extended to a real structure, the model would predict the highest tensile stress at the outer periphery of a bond, and oriented at 45° with the plane of the bond interface. This prediction is found to be in agreement with the bulk of fracture experience in shear-constrained semiconductors.