There are about 160 people living at Tjuntjuntjara. They speak a southern variety of the Pitjantjatjara language. They identify as belonging to a group of people known as ' (meaning "from the spinifex plains"). This group of people are among those that were removed from their homelands in the 1950s and 1960s due to nuclear weapons testing at Woomera Test Range. Most of the people now living at Tjuntjuntjara were previously living at Cundeelee, then a Christian mission, further to the west. Other communities of ' people include Oak Valley and Yalata, over the border in South Australia.