A method is developed for finding the stress distribution in a cracked body under longitudinal shear and applied to solve a number of problems. Stress solutions are obtained in closed form and discussed in connection with the Griffith-Irwin theory of fracture. The results indicate that current fracture-mechanics theories may be applied directly to longitudinal shear problems. More specifically, the character of the stress distribution near the vertex of a sector cylinder in shear is examined. The inverse half-power law of the stress singularity at a crack tip may be verified by taking a vertex angle of 2π. In addition, crack-tip, stress-intensity factors are defined and evaluated from a complex stress function in a manner similar to those previously given for extension and plate-bending problems. Results of such studies clarified the behavior of branched cracks and other crack systems of interest.