The NASDAQ exchange saw Facebook shares jumping more than 10% within minutes of making their stock market debut.
Facebook shares rose to $42, having been initially priced at $38 each, before falling back to trade flat.
Mark Zuckerberg, 28, who started Facebook while at university, remotely opened trading on the Nasdaq earlier.
He appeared via a video link from a celebration at the firm’s headquarters in California.
There had been a delay of about half an hour in the start of trading in Facebook shares, which analysts say reflected the huge demand for the stock.
The $38 initial share price values the eight-year-old social network site at $104 billion.
Strong demand had led the company to increase both the price and the number of shares available for sale.
Facebook’s owners are releasing just under a fifth of the company’s total shares, about 421 million, which could raise about $18 billion.
The site is largely used for social updates, and although Facebook has said its use on mobile devices are the key to new profits, analysts question how much room there is for advertising on such platforms.
Car giant General Motors added to those doubts by saying on Tuesday that it would no longer pay to advertise on the site.
Online strategy consultant Atul Chitnis said the question was whether Facebook had a strategy to bring advertisers in.
“My belief is that Facebook does have a strategy, they are ready with something they have not yet talked about,” he said.
“How effective it is we will have to watch and see.”
He also said he expected to see a “brief burst” of the share price going up and then “sinking again” in a couple of days.
Facebook’s valuation means the social network site is worth about the same as internet shopping giant Amazon, and more than the value of stalwarts such as Disney.
The initial public offering (IPO) of the shares is the third-largest in US history, after the financial giant Visa and General Motors.
Facebook employees had been up all night ahead of the event, taking part in a “hackathon” at the company’s headquarters in Menlo Park, California.
It is an event in which programmers work on projects and come up with new ideas.
Facebook’s profits are tiny in relation to its size – it makes about $5 a year for each of its 900 million users – and its plans to increase profitability are unclear.
Oliver Pursche, president of Gary Goldberg Financial Services, said ahead of the flotation: “We’re telling our investors to hold off.
“Number one, we don’t know what the guts and the balance sheet of the company looks like yet so that’s a big red flag for us. We want to understand the business before we tell people to invest.”
Facebook also faces concerns over privacy.
Indeed, on Friday a class action suit was brought against the company in the US for “improperly tracking the internet use of its members even after they logged out of their accounts”.
Facebook itself has previously warned about the possible impact of evolving legal protections across the world on consumer privacy, and specifically a revision to the European Union’s privacy laws.
Other internet companies have had mixed experiences when they have started selling shares.
Online games maker Zynga’s shares fell 5% on their first day of trading in December 2011.
But shares in business networking site LinkedIn more than doubled on their debut in May last year and are still trading well above that level, while Groupon shares jumped 30% on their debut in November.
However, they have since fallen back, particularly after the daily deals firm admitted in April that it had overstated its previous revenues and earnings.
Facebook’s flotation had an immediate impact on the value of these companies, as their share prices fell at the same time as Facebook’s fell back from its initial spike.
Groupon dropped 5.6%, LinkedIn fell 1.2%, while shares in Zynga were suspended after plunging more than 13% in a matter of minutes.
The new Facebook shareholders will not have much say in how the business is run.
The shares on offer are “A” shares, which carry one vote per share, as is normal, but the current owners’ shares are “B” shares, which carry 10 votes each.
They will control more than 96% of the votes after the flotation, with founder Mark Zuckerberg holding just under 56% of the voting power of the company.
Mark Zuckerberg, who owns about 25% of the company, stands to gain the most from taking Facebook public. Fellow founders Dustin Moskovitz and Eduardo Saverin will also become paper-billionaires overnight, as will Napster founder and former employee Sean Parker.
US venture capital firm Accel Partners and Russian internet investment group Digital Sky Technologies also hold significant stakes in Facebook, while software giant Microsoft and U2 frontman Bono also stand to make a huge profit on their investment in the company.