An analytical model of an axisymmetric eddy current ferrite-cored probe above a multi-layered conducting half-space has been developed using a procedure in which the domain of the problem is truncated radially. This means that solutions can be expressed in the form of generalized Fourier-Bessel series. The expansion coefficients are found by matching the field across the interfaces between the subregions of the problem. Initially, the magnetic vector potential of a simple circular current filament is expanded in a series form. The solution is then modified to accommodate an infinitely long coaxial ferrite core, and the principle of superposition is invoked to derive a coil field from the filament field in the presence of the core. Next, we consider a semi-infinite core and then one of finite length. Finally, the effects of a multi-layered conductor are included. Numerical predictions of probe impedance have been compared with experimental data showing excellent agreement.