Plate-form inclusions of shear type represent the mechanical aspect of many important processes, such as the formation of slip bands, twin bands and martensitc plates in crystalline materials. All these processes connect closely with fracture of materials. Analytical expressions for stress intensity factors of the crack near the inclusion have been derived by using dislocation theoretical method. Using the results of this paper, some aspects of the cracking due to a plate-form inclusion are discussed. The Hall-Petch relation of twin-fracture stresses can be obtained from the inclusion model, and the theoretical results are in good agreement with experiments.