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A method is proposed for determining the two-dimensional stressed state of a half space with a general rectilinear anisotropy. General representations of the complex potentials are obtained and studied, as well as expressions for the stresses and displacements, along with the boundary conditions for determining these functions. As an example, we solve for the stressed state of and calculate the stress intensity factors for a half plane (in the presence of a single elastic symmetry plane) with a circular (elliptical) hole and edge cracks. It is shown how the crack length, the closeness of a hole with a crack to the boundary, and the anisotropy of the material affect the stress concentration and stress intensity factors.