Eddy current techniques have been widely used in the NDE inspection of aircraft engine components. Depending on the flaw characteristics and specimen composition, various EC probe designs have been employed to achieve the maximum probability of detection (POD). Traditionally, the effectiveness of a probe design for a given inspection is determined experimentally. In particular, parameters such as probe types, operating frequency, scan spacing, etc. are evaluated experimentally in terms of POD. It is obvious that this is a costly way of defining inspection parameters. A more cost-effective alternative is to evaluate the test parameters through the use of numerical simulation. This can be done by casting the entire EC inspection process in terms of a numerical model governed by a set of integral equations. By computing the solutions to the integral equations, outputs in the form of impedance changes due to flaws can be used to generate the POD. Previously, we have introduced a modified version of the Hertzian magnetic potential approach for eddy current probe design [1]–[3]. In those papers, it was shown that the formulation can be used to solve problems with arbitrary geometries including geometrical singularities such as edges and corners. In the present paper, we have modified the boundary integral equations (BIEs) formulation for computing the impedance change in the presence of ideal tight cracks. Some unique features of this model include the allowance for arbitrarily shaped air core probes and test components that include singular geometries.