Bamber, along with serial killer Peter Moore and Douglas Vinter, argue that the whole life tariff is "inhuman".
The court has previously ruled that such sentences do not violate a prisoner's human rights, but the matter was referred to its grand chamber for the final say.
The ruling is expected at 09:30 BST.
The three men are among a group of 49 people in England and Wales who are serving whole life tariffs.
This means they cannot be released other than at the discretion of the justice secretary on compassionate grounds - for example, if they are terminally ill or seriously incapacitated.
They claim that being denied any prospect of release amounts to "inhuman and degrading" treatment and this is a violation of Article 3 of the European Convention on Human Rights.

Probably should have thought about that before they started murdering people then! Honestly, why hasn't someone sat him down and said "look, you murdered 5 members of your own family, why on earth would you think you have any rights to freedom as a result?"

Yes but Bamber is clearly a sociopath and should probably never be released. I have no problems with life tariffs. Otherwise the public will want the death penalty. The courts have not been extravagant and doled out life tariffs to every killer. So only 49 will never be released, which seems acceptable.

If he is so very clearly a sociopath who should not be released, there's no danger in a periodic review because he won't be released.

If, however, he is not so clearly a sociopath, we need to have periodic reviews for the same reason that we don't have capital punishment - the justice system makes mistakes. And rectifying a mistake should not be the job of a partisan politician who is subject to the whims and desires of that morning's headlines.

All they have to do is say that he gets a parole hearing after the first 25 years and every 10 years thereafter. But that would rampant softy-liberalism, wouldn't it?