The flood warnings on Monday covered much of Eyre and Yorke Peninsulas, and parts of the Flinders Ranges.
The State Emergency Service said multiple roads across those regions were either damaged or covered in debris.
"While widespread intense rainfall is not expected across the warning area, heavy rain with isolated thunderstorms is still likely," the SES said on Monday.
The Department of Transport and Infrastructure said a number of roads on Eyre Peninsula and across the state's north remain closed with others accessible only by four-wheel-drive.
Among those cut was the road between Pimba and Woomera after rain on Saturday washed away large sections of bitumen.
Department Chief Executive Tony Braxton-Smith told a parliamentary committee on Monday that crews were working to restore the Olympic Highway with the wash away also limiting access to Roxby Downs and the Olympic Dam mining community.
"As you know there's been record rains. I think it's been characterised as a one in 100-year event.," he said.
Mr Braxton-Smith said other roads to be impacted for varying periods included the Sturt, Lincoln and Eyre highways.
He said those roads were being progressively reopened.
After Saturday's heavy falls, the Bureau of Meteorology said widespread rain continued on Sunday with totals ranging from about 50 millimetres in a number of centres to a high of 108mm at Price on Yorke Peninsula.
Tumby Bay also received 90mm over the past 24 hours and Kadina 86mm.
Bureau meteorologist Vince Rowlands said such heavy rain across SA was not common in January with the last such significant event dating back to 1946.
It could result in many areas posting record rainfall totals for January with the unseasonal conditions the result of an upper level low and associated surface trough which formed over the west of the state and moved slowly eastwards.
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