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This paper describes a method for the efficient numerical evaluation of modal series, which are involved in the full-wave analysis of shielded vertical metallizations in the framework of the integral-equation method-of-moments approach. Generally, the modal series converge very slowly, when treated in its original form, and it makes the approach inefficient from a practical point-of-view. The proposed method for effective series summation is based on Kummer's transformation augmented with two additional techniques, which greatly enhance its efficiency. The two techniques have been developed based on the results of an investigation into the analytical, as well as spectral properties of the modal series. The method has proven to be very effective, especially in the full-wave analysis of very short vertical metallizations, such as via-holes, since the analysis can be based only on evaluation of the static part of the modal series. This feature makes the proposed method a good candidate for practical purposes, especially electromagnetic computer-aided-design tools.