In this work, a new technique is presented which will predict the path of a naturally growing crack near a rigid elliptical inclusion, where the stress field can be modelled as two dimensional. The technique uses a boundary integral approach to the solution of the stress field at the tips of the crack which is in general not straight, and is interacting with a rigid elliptical inclusion. The crack is parameterized as a cubic spline, and the results of both a Green’s Function solution to the interaction of a dislocation with an elliptical inclusion, and a first order perturbation solution to account for the generally curvilinear nature of the crack have been employed. The singular nature of the stresses is accounted for using a numerical technique which describes the distribution of dislocations along the crack as a piecewise quadratic polynomial to transform the problem’s resulting integral equations into algebraic equations well suited to a matrix-type solution. Results of each step of the analysis have been verified with previously published results, and with experimental results of a crack propagating near an open circular hole. New and significant results are also presented as paths of cracks interacting with inclusions of differing ellipticity ratios, and at different orientations with respect to the initial crack.