WASHINGTON—Joe Sullivan was sent away for life for raping an elderly woman and judged incorrigible though he was only 13 at the time of the attack.

Terrance Graham, implicated in armed robberies when he was 16 and 17, was given a life sentence by a judge who told the teenager he threw his life away.

They didn’t kill anyone, but they effectively were sentenced to die in prison.

Life sentences with no chance of parole are rare and harsh for juveniles tried as adults and convicted of crimes less serious than killing. Just over 100 prison inmates in the United States are serving those terms, according to data compiled by opponents of the sentences.

Now the Supreme Court is being asked to say that locking up juveniles and throwing away the key is cruel and unusual—and thus, unconstitutional. Other than in death penalty cases, the justices never before have found that a penalty crossed the cruel-and-unusual line. They will hear arguments Monday.