The eddy current NDE inversion problem is to determine the parameters of a flaw from the measured eddy current sensor impedance changes. Mathematically, this requires finding the transformation which gives the sensor impedance changes in terms of the flaw parameters, and then inverting this transformation. Finding the transformation is called the forward problem, and finding the inverse of the transformation is equivalent to the inversion problem. The principal difficulty in solving the forward problem is finding solutions to Maxwell's equations in the complex geometries involved. This paper describes a solution to the forward problem which is valid for ellipsoidal shaped void flaws in a non-magnetic conductor, and for flaw dimensions such that the incident field variations are at most linear over the region occupied by the flaw.