This paper presents a conductivity profiling technique of a graphite brick and a Finite Element (FE) model study of an eddy current (EC) probe, which may be used to inspect graphite bricks in an Advanced Gas-cooled Reactor (AGR) core. This work was initially concerned with investigation and optimisation of EC probes in terms of their sensitivity to the conducting graphite, particularly with depth, followed by the implementation of an optimised probe prototype, which was used to validate the FE model. The graphite inverse problems in this paper were solved using the measured data from a sample graphite brick and adapting an iterative inversion technique. During the inversion process two different approaches have been adopted: constrained and unconstrained along with two different initial estimates. The FE-based sensitivity study results show an average of 43.7 % sensitivity improvement compared with an existing probe and reasonable agreement between the simulated and measured data. The inverse solutions in this work show negligible effect on the accuracy of the reconstructed profile when applying different initial estimates within the algorithm. It was found that the constrained profiles yield a minimum profile error of 3 % compared with the experimentally-determined graphite electrical conductivity values.