Liberal leader Steven Marshall has declared a "new dawn" in South Australia after claiming victory in the SA election, with his party poised to form government for the first time in 16 years.

Key points: Liberal leader Steven Marshall claims victory in SA election

Liberal leader Steven Marshall claims victory in SA election Mr Marshall declares a "new dawn" after 16 years of Liberal opposition

Mr Marshall declares a "new dawn" after 16 years of Liberal opposition Labor leader Jay Weatherill congratulates Mr Marshall

Labor leader Jay Weatherill congratulates Mr Marshall SA Best looks unlikely to secure a seat as Liberal Vincent Tarzia sees off Nick Xenophon

Mr Marshall arrived to a rock star's welcome at the Liberal election function, walking to the stage to the sound of The Killers' song The Man.

"A massive thank you to the people of South Australia who have put their trust, their faith in me and the Liberal team for a new dawn, a new dawn for South Australia," he told cheering supporters at the Hackney Hotel.

"Can I thank all of my colleagues in the shadow cabinet, soon to be the cabinet. They have worked so hard.

"There have been some very dark days, in fact 1,460 days since the last election."

During his victory speech to the party faithful, Mr Marshall singled out Hartley MP Vincent Tarzia for praise, after the ABC's election computer predicted he would beat SA Best leader Nick Xenophon to claim the seat.

"It must have been a very big shock when you find out Nick Xenophon is running against you in Hartley," he said.

"It was not expected. I think most people at that point in time would have thought, this is not going to happen, I'm going to throw in the towel. Did he throw in the towel? No way."

Despite strong challenges from Labor and SA Best, Mr Marshall is predicted to easily secure his seat of Dunstan in Adelaide's east, with a swing of 2.5 per cent in his favour.

The ABC election computer called the election earlier in the evening, predicting the Liberals would win the 24 seats needed to form government in its own right.

Later, Labor leader Jay Weatherill conceded defeat, phoning Mr Marshall to pass on his best wishes.

Sorry, this video has expired Weatherill concedes defeat in SA election

"A few moments ago, I called Steven Marshall and conceded that he had won this state election," Mr Weatherill told supporters.

"I passed onto Steven Marshall my congratulations from our party, on his personal achievement, and also the achievement of his candidates, in winning their seats, and forming a government for the state of South Australia.

"I'm sorry I couldn't bring home another victory, but I do feel like one of those horses that has won four Melbourne Cups and I think the handicap has caught up with us on this occasion."

However, Mr Weatherill is almost certain to retain his seat of Cheltenham.

SA Best has so far fared nowhere near as well as predicted, with current indications it will struggle to win a Lower House seat and leader Nick Xenophon unlikely to win his battle for Hartley.

Liberal candidate Vincent Tarzia thanks supporters after seeing off Nick Xenophon. ( ABC News; Matthew Doran )

A defiant Mr Xenophon is still predicting his party will have a presence in Parliament.

"This is, this is not the beginning of the end, it's actually the end of the beginning. Because I think we're going to see some very interesting things happening," he said.

"Let's wait and see what happens... we won't have an idea for three or four days as to what is happening."

The election appears to have thrown up some other surprising results.

The ABC's election computer is predicting Labor-turned-independent Frances Bedford will retain her seat of Florey in Adelaide's north-east.

And Mount Gambier Liberal-turned-independent Troy Bell, who is facing corruption charges, also looks set to retain his seat.

Labor incumbent Leon Bignell is in a tight race in his seat of Mawson.

And despite ABC election analyst Antony Green calling the seat of Frome to remain with independent MP Geoff Brock, he's refusing to claim victory.

"I've still got the pre-poll to come in at this stage and I understand there's still a bit in there," he said.

"It's looking very good for us, I'm optimistic as I always have been, but I'm not going to call it."

Mr Brock admitted he was sad to relinquish the ministerial position he gained when backing Labor at the 2014 election.

"I give the guarantee that I'll be busting my boiler to make certain that the continuation of the focus on regional SA and Frome is before this new government," he said.