She said her family had Aboriginal lineage and her "great x 8 grandfather" Joseph Dickson, Chamberlain of Finance from the first day of the council, had helped build the cemetery.
Wendy Coker Turville said her family had been buried at the beautiful spot for six generations: "I go out there all the time to visit my ancestors when I can, I would like them to be there for my family and for our future history."
Trina Robert Kluin added: "My great great grandmother is buried there. How sad this has happened."
Bronwyn Kelly, from the campaign group Save Waverley Cemetery, said she had been warning of a possible collapse for years.
"Waverley Council has been repeatedly warned over the past six years about the instability of Waverley Cemetery's 17m-high gully tip fill area, over which well more than a million visitors walk each year," said the former councillor.
"Despite numerous warnings from independent engineers and Save Waverley Cemetery, the council has outright refused to take remedial or preventative action.
"The council has insisted that all it needed to do was 'monitor' the situation - as if simply watching this massive unstable site of at least 70,000 cubic metres of unretained, poorly compacted fill while it slowly crumbles and falls, constitutes duly diligent asset and risk management.
"It really is culpable behaviour."
But a rival group, Residents for Waverley Cemetery, has criticised the Save Waverley Cemetery group for promoting the building of a pavilion to stabilise the area, saying it would not have survived the weekend's wild weather.
"The landslip following the storms this weekend demonstrates the folly of considering building a pavilion or other structure in that area," Sam Baxter wrote on the Facebook page.
Waverley Council told the Daily Telegraph yesterday: "Council has undertaken regular monitoring of the site in response to the consultant's recommendations. No movement was detected prior to the extreme wave activity over the weekend."