Some forward and inverse problems related to layer sizing in eddy current nondestructive evaluation (NDE) were examined and experimental tests were done. An air-core or ferrite-core eddy current probe coil above a half space is considered. The half space's conductivity changes only as a function of depth, but otherwise it is arbitrary. A numerical method for the computation of coil impedance based on the exact solution of Cheng, Dodd and Deeds (International Jour. of Nondestructive Testing, 3, 109-130,1971) is described. Also, for a specific conductivity profile involving the hyperbolic tangent function, the exact solution for the impedance is given. This exact solution was used in testing the convergence of the numerical method mentioned above. Experimental tests were done on model systems designed to imitate continuously changing conductivity profiles. An analytic solution is given that determines the electric and magnetic fields for a single turn coil that contains a ferrite core and that is placed above a conducting half-space. In the last two parts of the dissertation, we consider the determination of the half-space's conductivity profile from frequency dependent eddy current measurements. Experimental tests were done on single discrete layers and also on model systems designed to imitate continuously changing conductivity profiles.