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This work deals with the 3-D numerical modeling of the interaction of an electromagnetic field with laminated carbon fiber reinforced polymer composites (CFRPs) for nondestructive testing applications. A model based on an integro-differential formulation in terms of the electric vector potential is developed for eddy current computation in CFRPs. It accounts naturally for the electric current and magnetic flux conservations. Moreover, it allows confining the modelling to the electrically conductive parts of the device, and, for thin structures, it can be reduced to a quasi-two-dimensional case involving only the normal component of the electric vector potential. To avoid storing the dense matrices resulting from the discretization of the integral terms, an iterative method is proposed to solve the resulting algebraic system; this results in a considerable economy in memory space and gain in computation time.