The stress state developed in a thin adhesive layer bonded between the semiconductor chip and the leadframe and subjected to a shear loading is investigated. The boundary element method (BEM) is employed to investigate the behavior of interface stresses. Within the context of a linear elastic theory, a stress singularity of type $gamma^{lambda=1}$(0<1<1) exists at the point where the interface between one of the rigid adherends and the adhesive layer intersects the free surface. Such singularity might lead to edge crack or delamination.