Yes, Joint Base Elmendorf-Richardson is a pet friendly installation.

You are allowed up to two pets, with a third being approved via approval of a Pet Waiver.

The following breeds of dogs (including mixes of these breeds) are prohibited:  Pit bull (American/English/Irish Staffordshire Bull Terriers), Rottweiler, Doberman Pincher, Chow, and wolf hybrids. In addition, the following animals are prohibited from being kept as pets: farm, ranch, or wild animals, marsupials, primates (monkeys and apes), ferrets, raccoons, hedgehogs, pot-bellied pigs, exotic felines, squirrels, skunks, rodents (rats and mice), reptiles, snakes, spiders, and any animal requiring a permit from the Fish and Wildlife Service.