In this work we have proposed a model, based on the semi-analytical Boundary Element Method (BEM), that predicts the perturbation magnetic flux density component arising due to a narrow opening embedded flaw present in an electrically conductive medium of finite thickness. We have derived the results based on the classical dipole model of flaws (scattering source) typically encountered in eddy current based nondestructive testing and evaluation. The problem that we have modeled is the field scattered by a rectangular flaw embedded in a conductive material, achieved by stacking two electrically conductive plates that are non-magnetic. A cylindrical coil scans the flaw. The excitation field varies time harmonically. The experimental verification was carried out by utilizing a highly sensitive giant magneto-resistive sensor. We have compared the model predicted results to the experimental study with a good agreement.