The problem of a symmetrical star-shaped array of curvilinear cracks in an infinite isotropic elastic medium is reduced, by using the complex potential technique of Muskhelishvili [1], to a complex Cauchy-type singular integral equation on one of the cracks together with a complex condition of single-valuedness of displacements. This equation can be solved numerically by reduction to a system of linear equations after application of the Lobatto-Chebyshev numerical integration method for the approximation of the integrals involved in it and an appropriate selection of the points of collocation. An application to some cases of circular-arc-shaped cracks is made.

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