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In this study, an axisymmetrical problem for a penny-shaped crack under radial shear is considered. The crack is located parallel to the surface of a halfspace, which is subjected to initial stress parallel to the crack plane. An approach proposed by Guz (1983) in the framework of the three-dimensional linearised solid mechanics is used. Analysis involves reducing the problem to a system of Fredholm integral equations of the second kind, where the solutions are identified with harmonic potential functions. The representations of the stress intensity factors KI and KII near the crack edges are obtained. These stress intensity factors are both influenced by the initial stress.