The singular stress field generated at the intersection of a grain boundary and a stress-free edge is investigated for a columnar polycrystal. An idealized, plane strain geometry that embeds four columnar cubic crystals within an effective isotropic media is analyzed. This idealized problem permits a detailed finite element analysis that can resolve the nature of stress singularities. Particular emphasis is placed on characterizing the magnitude of the stress fields and defining the size of the region dominated by the singularity. The effects of crystal and grain boundary orientation combinations and crystal properties are examined.