Inversion of eddy-current data and the reconstruction of flaws is the preeminent problem in electromagnetic nondestructive evaluation(NDE).This places a premium on developing good forward models for computing field-flaw interactions.Material flaws or defects are usually very thin compared with the characteristic length.But it generates singular eddy current density and makes numerical simulation very difficult.I shall talk about the simplification of the eddy current model and present some numerical experiments using finite element method.