Mr Musk, who is being sued by Tesla shareholders arguing he manipulated the firm's share price, has said he cannot get a fair trial in San Francisco.
He wanted the trial to take place in Texas - where he has moved Tesla's headquarters - but that was rejected.
A jury has been selected, after jurors completed a pre-trial questionnaire.
The case centres on 2018 tweets, saying that he would take Tesla private. US regulators removed Mr Musk as Tesla chairman because of the posts.
On 7 August 2018, he tweeted that he had "funding secured" to take the carmaker private in what would be a $72bn (£58.7bn) buyout.
In a second tweet, Musk added that "investor support is confirmed," and that the deal was only awaiting a vote by shareholders. No such deal went ahead.
"The claim is that the investors felt that they were defrauded by Musk's tweet, that he was considering taking Tesla private and critically, that he had funding secured for it," Robert Bartlett, law professor at the University of California, Berkeley, told Reuters.