Facebook shares have fallen sharply for a second day, wiping billions off the notional value of the company.

Facebook Inc. Chief Executive Mark Zuckerberg has sold 30.2 million shares and director Peter Thiel has sold 16.8 million shares of the social-networking company, according to securities filings published late Tuesday.

The sales confirm plans detailed in a prospectus before Friday's $16 billion IPO. Zuckerberg sold 30.2 million shares at a price of $37.58 for gross proceeds of $1.13 billion; Thiel sold 16.8 million shares for gross proceeds of $633 million.

The social network stock, branded 'FB' on the Nasdaq exchange, fell more than 12% per cent on opening on Tuesday, before rallying to 4.2 per cent down within 90 minutes of opening.

Facebook shares fell 11 per cent on their second day, after the hype surrounding the firm's flotation on Friday evaporated.

Shares were initially priced at $US38, valuing the company at around $US104bn, but doubts have persisted about whether the company can convert its huge global following into revenue.

Facebook now has more than 901 million users worldwide, but some have questioned its ability to deliver that reach into a tangible return for advertisers.

General Motors cancelled its $US10m marketing contract with the social network last week, claiming its adverts had little impact on its consumers' decisions to buy cars.

Investors said the firm would have to justify its valuation and demonstrate its maturity.

David Rolfe, chief investment officer at Wedgewood Partners, said: "Wall Street is a severe task master and they're going to want to see quarterly results, then guidance, then subsequently they're going to want to see that guidance beaten, and then the guidance raised."

Questions have also been raised about the decision to price opening shares at $US38, up from the initial range of $US28-35 per share.

Financial blogger and chief market strategist at Fusion IQ in New York, Barry Ritholtz, blamed the company, its underwriters, and the exchange itself.

He said: "What we see are a series of bad decisions made by Facebook's executives going back many years. The insiders got greedy, too clever by half, in how they used secondary markets. They picked a bad banker and an awful exchange."

Founder Mark Zuckerberg rang the opening bell by remote internet link from California on Friday, surrounded by thousands of cheering Facebook staffers.

He announced his marriage to long-term girlfriends Priscilla Chan on Saturday by updating his relationship status on the social network.

The company's plunging share price since will make for uncomfortable honeymoon viewing.