Based on the solution of an internal crack, we have investigated the elastic interaction of a screw dislocation and cracks emanating from an elliptic hole by using a conformal mapping technique. We have derived the stress field, the image force on the dislocation, the stress intensity factor at the crack tip, and the crack extension force. From the image force, we find the unstable equilibrium positions of dislocation. It is possible to form a plastic zone from the region containing the unstable equilibrium position by collecting dislocations. By extending the concept of the unstable equilibrium position, we also develop the dislocation emission criterion. It is found that the critical applied stress for dislocation emission is dependent on the geometry of the crack. In addition, we also find that the elliptic hole prefers to emanate double cracks. Finally, it is worthwhile to mention that the mapping function cannot be arbitrarily chosen.