The stress concentration due to cusp-like flaws along a rough surface is important to the understanding of flaw initiation at material surfaces under environmental corrosion. This paper is part of a new effort to develop theoretical models for various micromechanical failure processes in thin film devices, such as the nucleation of surface cracks in coatings of magnetic storage devices under sliding contact. The stress field near an isolated surface cusp is studied using complex variable methods. Calculations indicate that the cusp induces the same stress singularity with similar stress intensity factors as a surface crack, thus establishing a role of surface cusps as precursors or nucleation sites for macroscopically observable cracks.