Artificial cracks are required for heat exchanging surface and/or flow paths in the hot dry rock reservoirs. Fracture mechanics is the only methodology that has been found effective in evaluating the size of artificial cracks, the surface area of the heat exchanger. In this study, fracture mechanics with boundary element method based on the displacement discontinuity formulation is presented to solve general problems of interaction between artificial hydro-fractures and discontinuities that are in the reservoir. The numerical results are in good agreement with the results brought in the literature. The comparison of numerical method with exact solution shows a good performance of the method in the case of interacting cracks too.