The Law Lords are to consider whether the cases of six Iraqi civilians who died at the hands of the British are subject to UK human rights law.
Mr Shiner is calling for an independent inquiry into the deaths
The test case is examining the death of Baha Mousa and also those of five other Iraqis shot during patrol operations.
The highest court in the country will decide if British troops in Iraq are subject to the Human Rights Act and the European Convention on Human Rights.
The case will be heard by the Appellate Committee of the House of Lords.
If the Law Lords decide the troops are subject to these rules, they will then decide whether the government has failed in its obligation to conduct an independent and effective inquiry into the incidents.
The case is being brought a number of organisations, including Amnesty International, the Association for the Prevention of Torture, the Bar Human Rights Committee and the human rights group Liberty.
IRAQIS KILLED BY BRITISH
Baha Mousa, 26: Died in British custody, September 2003
Hazim Al-Skeini, 23: Shot in the street, August 2003
Muhammed Salim, 45: Shot at his brother-in-law's home, November 2003
Hannan Shmailawi: Killed by machine gun fire from outside her home, November 2003
Waleed Sayay Mezban, 43: Killed driving home from work, August 2003
Raid Al-Musawi, 29: Iraqi police officer who died nine weeks after being shot, August 2003
Before the hearing began pictures and medical evidence relating to the 26-year-old, who died in British custody in Basra in 2003, were shown at a press conference by Phil Shiner of Public Interest Lawyers, who is Mr Mousa's lawyer.
The photographs and records show 93 injuries including a fractured nose and four broken ribs, severe injuries to his wrists and a ligature around his neck.
Mr Shiner said: "We're not just talking about nuanced degrading treatment, this is torture by any definition of that word.
"And we're not just talking about torture, we're talking about the techniques the Heath government banned, such as hooding, sleep deprivation, stressing, food deprivation and white noise."
Seven UK soldiers were accused of abusing Iraqi detainees in Basra in 2003, including Mr Mousa, and after a six-month long court martial hearing at Bulford Camp, Wiltshire, six men were cleared of all charges.
A seventh man pleaded guilty to one charge, although he was cleared of two others.
Both Mr Shiner and Liberty are calling for an independent inquiry to hold the government and the higher levels of the British military to account.
The High Court and Court of Appeal have previously ruled that the Human Rights Act applies in situations where an individual is detained by a British authority.