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The applicability of using flat composite plates and hollow core composite cylinders for moisture absorption testing of unidirectional glass/polymer composites used in high voltage composite (non-ceramic) insulators was examined. Two main issues were addressed in this work. First, the effect of specimen geometry (cylinders vs. plates) on moisture absorption by the composites was investigated both numerically and experimentally. Both classical Fickian and non-Fickian diffusions were considered. Subsequently, hollow core cylinders made up of ECR (low seed)-glass fibers and epoxy resin were tested for their high voltage properties under controlled moisture diffusion conditions. The specimens were exposed to warm, moist air and their high voltage properties were ascertained using a modified version of the ANSI test (standard C29.11 Section 7.4.2) for water diffusion electrical testing. It was found that the behavior of the hollow core cylinder and flat plate composite specimens subjected to moisture compared reasonably well experimentally and very well numerically. From the high voltage tests, a direct correlation was found between the amount of moisture that had been absorbed by the specimens and the amount of leakage current that was detected. It was shown that using the thin walled composite cylinders leakage currents could be predicted based on the amount of absorbed moisture in the insulator composites. The predictions can be made based on relatively short term moisture data even if the diffusion process in the composites is anomalous in nature with long times required for full saturation. After additional verifications, considering other composite systems, the hollow core cylinder testing under controlled moisture and high voltage conditions could become a screening test for selecting suitable glass/polymer composites for insulator applications.