This paper proposes a strategy for the fast simulation of eddy current testing signals due to a conductive crack of arbitrary width. To cope with a crack of width less than that selected for establishing the database, which is necessary in the fast-forward analysis scheme proposed by authors, a new finite element is introduced to treat the case when the crack boundary is contained in the element. By using such a new element, the fast-forward analysis scheme becomes suitable for the reconstruction of both the shape and width of a planar crack. It is verified that such a multiple material element is efficient for an ECT sensor inducing eddy current parallel with the crack surface. For the case with perpendicular eddy current component, however, the approach is not valid because of a scalar potential jump at the crack surface. Finally, the reason of such a singularity is investigated through numerical simulations.