This article presents the modeling of non-destructive testing systems containing magnetic materials using a fast numerical method. Its main aim consists of correcting the half analytical expression of the impedance variation, formulated by some authors, caused by the presence of a conducting plate below of an absolute ferrite core probe. The obtained results of this correction are found to be consistent and satisfactory comparatively to those of finite element method. It also deals with the study the method rapidity by comparing its simulation time to that of the finite element method. As result, the proposed method is found to be very fast and a very short simulation time is required to calculate the sensor impedance. Indeed, for the studied system the coupled circuit simulation time is lower than 1.09 s. This study is appreciable, since it permits to solve quickly the inverse problem by expressing the physical and geometrical features of the material or defect according to the measured parameters. More importantly, this method is applicable to any axi-symmetric systems and can be adapted for the simulation of three-dimensional configurations.