Musk, often the center of controversy, did not prove he had the funds to finance the operation - despite tweeting "funding secured".
Isaacs accused Musk of making false and misleading statements to inflate Tesla's stock price, and that Tesla "doubled-down" on those statements by failing to correct them.
The two lawsuits filed by Isaacs and William Chamberlain on Friday alleged that Musk and Tesla's behaviour following the tweets violated U.S. securities law, and artificially inflated the company's share price.
Mr Isaacs and the second plaintiff, William Chamberlain, have alleged that Tesla's stock price was artificially inflated and federal securities laws had been breached. The company is based in nearby Palo Alto, California.
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Short-sellers make a profit by borrowing overpriced shares, selling them and then buying them back at what they hope will be a lower price. But in the days since, it has lost most of those gains, reacting, at least in part, to reports from Bloomberg and the Wall Street Journal that the federal Securities and Exchange Commission is investigating Musk's claim.
Such investors have always been an irritant for Musk, who has sometimes used Twitter to criticize them.
They have cited as evidence Musk's tweet that came on August 7 and the very next day, Tesla shares went up by around 13%.
According to the complaint, Isaacs bought 3,000 Tesla shares on August 8 to cover his short position, or bet that the price would decline, in the company.
But Isaacs said Tesla's and Musk's conduct caused the volatility that cost short-sellers hundreds of millions of dollars from having to cover their short positions, and caused all Tesla securities purchasers to pay inflated prices.