The whales, which can weigh up to 50 tonnes, were found at low tide by residents on Parara beach, about 150 kilometres northwest of Adelaide.
"We're not sure why they beached," a Department of Environment official told AFP.
"A theory is that one was ill and moved to shallow waters and then called out to fellow pod members who followed it in."
A local fisherman suggested they could have been chasing a school of salmon.
"I haven't seen a marine event like this in South Australia since the mass stranding of 58 dolphins at Nepean Bay in the 1990s," she told the Adelaide Advertiser.
The department official said police and the council were considering their options on how to handle the carcasses, which were now in shallow waters and could attract sharks.
"It's a very big logistical task," the official said.
Sperm whales is the largest of the toothed whale species and can grow up 16 metres (52 feet). It has the largest brain of any known animal currently in existence.
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