In this paper, the stress functions for a half-infinite anisotropic plate with a crack parallel to the free edge are obtained. These functions, which must be satisfied the boundary conditions on the free edge, are constructed by superposition of a series of stress functions for infinite anisotropic plates with a crack. It is learned that the obtained stress functions provide finite stress concentration in the assumed fracture process zones and generate normal stresses along the edge of the

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... , which is corresponding to internal pressure. Two numerical examples using the obtained functions are shown. The first is for the analysis of a rock material with a crack subjected to internal pressure. The second is for the analysis of the ground protuberance problem by grouting. The results suggest that the proposed functions be applicable to the practical engineering field.