This paper is concerned with the computation of the thin-skin solution for eddy current distributions induced in the presence of surface breaking flaws. Earlier work [1], [2], [3], [4] dealt with cases where the distribution induced in the absence of a flaw was uniform. An unfolding technique was developed which reduced the determination of the surface field to a classical two-dimensional potential problem. Exact solutions were obtained by complex potential methods for circular-arc cracks in [1], [2] and for rectangular and triangular cracks in [3], but the main focus of attention in this last work was on semi-elliptical cracks since it is found in practice that many surface fatigue cracks grow with a plan form which can be closely approximated by a half ellipse. This case was not amenable to exact treatment, but the introduction of elliptic co-ordinates allowed a Fourier series solution to be calculated.