Most damage happened along the city's beachside and southern suburbs, and up to 30,000 homes and business have lost power, while in Happy Valley a 50-foot tree has fallen on a house.

The State Emergency Service has responded to hundreds of calls of fallen stobie poles, fallen trees and other storm damage.

Driver Darren Paynter told ABC News his truck was bowled over by a strong gust of wind at Harbour Town near Adelaide Airport.

"I drove into McDonald's this morning, out to do a delivery and get some breakfast, and as I got back into my truck the wind blew it over," he said.

The wild weather has also forced the closure of four metropolitan jetties, at Semaphore, Grange, Henley and Largs Bay.

The Department for Transport, Energy and Infrastructure said the jetties would remain closed until further notice to ensure public safety, with barriers being set up to prevent public access.

"There are numerous reports of power lines down and tree branches falling," police said.

A number of roads were reported to be blocked by falling trees and other debris.

However, emergency services said there were no immediate reports of extensive damage or injuries.

ETSA Utilities said it had all available crews working to restore power.

“Winds gusting up to 100 kilometres an hour, lightning strikes and sheet rain have all impacted the network,” said Sue Filby, general manager services.

“Much of the damage in Adelaide has been caused in a half hour burst of severe weather this morning.

“We have had at least 10 feeders impacted in the metropolitan area and about 100 outages in total affecting as many as 18,000 customers across the state.”

Ms Filby urged customers to contact ETSA Utilities on 13 13 66 to report faults.

The weather bureau issued a severe weather warning today for Adelaide and parts of South Australia.