Nonconjugated conductive polymers absorb radioactive iodine, therefore are useful for protection against nuclear radiation. These polymers have at least one double bond per repeat unit. The ratio of the number of double bonds to the total number of bonds along the polymer chain is less than half. Examples of nonconjugated conductive polymers include: cis-1,4-polyisoprene (natural rubber), trans-1,4-polyisoprene (gutta percha), polybutadiene, polydimethyl butadiene, poly(b-pinene), styrene butadiene rubber (SBR), polyalloocimene, polynorbornene and many others. Through interaction with iodine atoms the double bonds in the nonconjugated polymers transform into radical cations leading to a dark color. The iodine atoms remain (immobile) bound to the polymer chain through the charge-transfer interaction, these polymers are very inexpensive and can be easily processed into any shape, structure and size. Therefore, these are useful for protection against nuclear radiation including radioactive iodine. These polymers when used as a thick cover can provide safe storage of nuclear waste materials including spent fuel rods.