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A linear elastic, anisotropic plate, which can contain multiple, rectilinear cracks is considered. It is assumed that the cracks are small in comparison with the distances between the cracks and the distances between the cracks and the boundary of the plate. It is assumed also that the loads applied to the boundary of the plate and the displacements of the boundary are measured in a single static experiment. A method for the cracks identification using the known overdetermined boundary data is developed. The developed method is based on the reciprocity gap concept, generalized functions theory and methods of cluster analysis. Numerical examples illustrating efficiency of the developed method are considered.