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Non-metallic structural materials that act as an electrical insulation are needed for cryogenic power applications. One of the extensively utilized materials is glass fiber reinforced resins (GFRR) and may also be known as GFRP and FRP. They are created from glass fiber cloth that are impregnated with an epoxy resin under pressure and heat. Although the materials based on GFRR have been employed extensively, reports about their dielectric properties at cryogenic temperatures and larger thicknesses are generally lacking in the literature. Therefore to guide electrical apparatus designers for cryogenic applications, GFRR samples with different thicknesses are tested in a liquid nitrogen bath. Scaling relation between the dielectric breakdown strength and the GFFR thickness is established. Their loss tangents are also reported at various frequencies.