Facebook shares ended their first day of trading at $38.23, barely above the company's initial pricing of $38.
Shares in the social network rose more than 10% to $42 within minutes of trade beginning, before quickly falling back.
Later gains were wiped out too at the end of a volatile day's trade, as the firm's debut on the Nasdaq exchange was also delayed by a technical glitch.
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.
The $38 share price values the eight-year-old social network site at $104bn (£66bn).
There had been a delay of about half an hour in the start of trading in Facebook shares, caused by a technical problem, which analysts say reflected the huge demand for the stock.
During this time, investors were unsure whether their buy and sell orders had actually gone through. The Nasdaq later said it intended to reach a resolution for orders entered in that period through an "offline matching process".
When trading did get underway, more than 566 million shares in the company changed hands, a record volume for US market debuts.
'Tripped on red carpet'
Most analysts had expected the shares to experience a first-day bounce.
"This starlet tripped on the red carpet. That's clear," said Max Wolff, senior analyst at Greencrest Capital.
He added that the only reason the shares did not fall below the offer price was because underwriters stepped in to buy the stock.
"This is exactly what the underwriters are supposed to do. However, if the company is trading near $40 with assistance then the implied valuation is lower."
Strong demand in the run-up to the flotation 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 $18bn.
The initial public offering (IPO) of the shares is the third-largest in US history, after the financial giant Visa and General Motors.
Facebook's $104bn 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.
Profits and privacy concerns
The site is largely used for social updates, and although Facebook has said its use on mobile devices is 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.
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, told the BBC 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."
Henry Blodget from Business Insider, a blog about internet businesses, said: "A lot of the Facebook bulls will say this company is going to be bigger than Google.
"But Facebook right now is one-tenth [of] the size of Google in terms of revenue, Google has more cashflow than Facebook has revenue, and Google was growing faster at this stage of the company than Facebook is. So I don't think that's a safe assumption to make."
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.
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.
Mr 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.