Police found the boys Saturday after an adult older brother told an off-duty officer at a grocery store about the squalid living conditions.
When police arrived at the home they found the children inside two cribs that had been wired together and sealed by plastic crates. Roaches filled the cages, which contained a blanket and small mattress stained with feces and urine.
Louis and Estelvina Rodriguez of Phoenix were arrested on suspicion of child abuse and kidnapping.
Authorities have not as yet elaborated on why kidnapping is part of their investigation.
The twins, who police said appeared to be healthy and well-fed, were placed in state custody, as was their 8-year-old brother, who neighbors said enjoyed more freedom.
"They were happy to see us and opened their arms wide, reaching out to be held and picked up," police Sgt. Jacqui MacConnell said.
Investigators believe the boys were released from the cages for a few hours a day when their mother returned from work.
Estelvina Rodriguez, 42, told police her 69-year-old husband wanted the active boys in cages because he suffers from health problems and couldn't keep up with them. She said they were trying to control the children, not punish them.
"Mom reported that the kids once got outside the house and were bitten by a dog," Sgt. Randy Force said. "She said they kept the kids in the cage for their own protection."
The couple each were being held on $243,000 bond.
The boys couldn't speak and aren't yet toilet-trained, police said.
"They can't talk," said Edna White, who has lived next door to the family for 27 years. "When they tried, just noises would come out."
State Child Protective Services officials received one complaint alleging the boys were neglected in 2001, but child-welfare workers visited the home twice and reported the children were outside playing, in good health and good spirits, agency spokeswoman Liz Barker said.
By Beth DeFalco