The State Emergency Service has responded to 900 jobs across the state, caused mostly by damage from fallen trees.
The worst of the weather struck Adelaide early on Monday, with storm activity returning later in the day.
SES deputy chief Liz Connell said about half of outback roads were currently closed and teams from the Country Fire Service had come to help.
Regional hospitals of Orroroo and Booleroo Centre were running on generators.Â
"The overwhelming number of jobs have been call outs for fallen trees which have blocked driveways and roads and have also brought down powerlines which are causing thousands of homes to be impacted," she told reporters on Monday.
A severe thunderstorm warning was issued for people in Yorke Peninsula, Flinders, Mid North, Kangaroo Island and North East Pastoral districts, but was cancelled on Monday afternoon.
The Bureau of Meteorology said they might redevelop with heavy rainfall overnight.
The Bureau of Meteorology's Hannah Marsh said more than 50mm of rain had fallen in Adelaide since Saturday, double the city's December average.
"The intensifying low pressure system over the (Great Australian) Bight will remain near stationary for a few days which is going to result in further shower and thunderstorm activity," she said.
Ms Marsh said large hailstones and winds of up to 90km/h were recorded in parts of the state.
There had also been more than 20,000 cloud-to-ground lightning strikes since Sunday.
SA Power Networks said more than 33,000 properties remained without power on Monday afternoon, with outages stretching from the mid-north, down Yorke Peninsula, through the Adelaide Hills and across the state's southeast.
15°C