Denise, According to BringFido: " Small pets are allowed in the caverns as long as they are carried for the duration of the tour. Pets of all sizes are allowed on the Luray Cavern grounds. There is not onsite kennel for pets. Dogs must be leashed at all times." I would call ahead to confirm this is still the policy. See: https://www.bringfido.com/attraction/13222 Service animals would be allowed.
I think they'd be freaked out underground for so long, and there are no facilities or place they could relieve themselves inside the caverns themselves.
Signs say no animals, though service dogs are most likely an exception
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