Knowledge of the behavior of the stress field in the neighborhood of cracks and sharp corners is important for many theoretical and practical reasons. In an earlier paper the authors examined the behavior of the stress field near the edge of an elastic wedge of arbitrary angle with stress-free boundary conditions prescribed on both surfaces (Karp and Karal, 1962). Other types of boundary conditions, such as those representing rigid and lubricated boundaries, were not considered. In the present paper these boundary conditions are now studied, and the behavior of the stress field in the neighborhood of the tip is determined. In addition, the stress behavior is examined when two different elastic media meet at a sharp edge.