Composite materials in the form of fiber-reinforced matrix materials as, for example, graphite-epoxy, are being increasingly used in critical structures and structural components because of their high strength-to-weight ratio. In order to assess the integrity of these structures, it is necessary to employ suitable methods for quantitative nondestructive evaluation (NDE). One such method uses electromagnetics (eddy-currents), but the problem is that composite materials are inherently anisotropic, which means that much of the classical eddy-current technology and design procedures are not applicable. In this paper we compute fields by applying a rigorous model of electromagnetic interactions with graphite-epoxy composites, which is based on a continuum approach. In this approach the graphite fibers produce a macroscopic conductivity tensor that has different conductivities in the directions parallel and transverse to the fibers.