This is according to the Socio Economic Right Institute on Friday.
"The families of the deceased will claim for loss of support and general damages," said their attorney Nomzamo Zondo.
She said the damages were estimated to be R1-million per family but it could be more.
Zondo said most of the mineworkers killed at Marikana were the sole breadwinners in their households.
"Their family members have suffered irreparable loss of support following their deaths at the hands of police officers," Zondo said. "Many of the family members suffered severe emotional shock when they heard of the killing of their relatives, and now suffer from depression."
Zondo said some family members suffered miscarriages while others died upon hearing of the killing of their relatives.
She said notices had been served on the police in terms of section three of the Institution of Legal Proceedings Against Certain Organs of State Act.
Payment to be made in 30 days
The Act requires payment to be made by the police within 30 days of receiving the claim, failing which the Socio Economic Right Institute would activate court proceedings against the police.
On August 16 last year 34 striking mineworkers were shot dead and 78 were injured when the police opened fire, allegedly while trying to disperse a group which had gathered on a hill near Lonmin's Marikana mine outside Rustenburg.
Ten people, including two police officers and two security guards, were killed near the mine in the preceding week.
The Farlam commission is holding hearings in Rustenburg, as part of its inquiry into the 44 deaths during the unprotected strike at Lonmin's Marikana mine.
Zondo hoped the Marikana commission of inquiry would make some important findings about what exactly happened on August 16 and in the days leading up to it.
"However, our clients believe that the South African Police Service used disproportionate force at Marikana that was unlawful, and that this use of force resulted in the deaths of their loved ones," she said.
"They are accordingly entitled to reparations for the loss of support and general damages incurred as a result of the killings." – Sapa