Two of the protestors were killed and a number were severely injured, assaulted and unlawfully detained by police during the protest, the 22 claimants' lawyers Leigh Day said.
The mine was owned at the time by Xstrata which was taken over by Glencore in a 2013 company merger.
Lawyers for the Peruvian villagers said they essentially alleged the miner was liable because it had provided significant assistance to the police and failed to take reasonable steps to prevent the use of excessive force.
Glencore said Xstrata was not responsible for police actions, Reuters reported, and noted that the lawsuit did not allege that Xstrata or the mine's private security force harmed anyone.
The 10-day hearing begins on Monday and the case will be determined under Peruvian law, Leigh Day said.
Tintaya ceased operations in 2013.
