The eddy current testing method is widely used to evaluate conductive pieces. This method requires an adequate mathematical model which is able to describe the complicated interactions between the source and induced currents, primary and secondary, the fields and the flaws in materials. This paper describes a model which predicts the apparent changes in the impedance of an absolute ferrite-cored probe in axially symmetric non destructive testing (NDT) configurations. Originally, this model is based on coupled electromagnetic quantities principle. To include the contribution of the magnetic environment, the state variable chosen is the current because the magnetic magnetization is replaced by the fictional equivalent currents. The obtained modelling results are validated by comparison to finite element computations. Once validated, the suggested model is not only applied to calculation of probe's impedance in the presence of a defect inside the load but it is also applied to determine geometrical and physical characteristics of the eddy current non destructive testing (ECNDT) device. This half-numerical technique with a very weak time of simulation can be used for the design of new probes and offers a simple solution to the inversion problem. The model is implemented within a software tool (CECM: coupling electromagnetic circuits method) developed in MATLAB environment.