Images of the crash, which occurred at 11.30pm local time, show the cabin of the Asiana Airlines Flight 214 Boeing 777 completely burned out, with its tail snapped off.
The plane was travelling from Seoul, South Korea. According to the Daily Mail, the two dead both had Chinese passports. One has been identified as a woman, the other a 16-year-old girl.
US Federal Aviation Administration spokesman Lynn Lunsfor told AFP the airport has been closed until further notice.
Passenger David Eun, an excutive for Samsung, tweeted a picture of people jumping out of the plane's emergency inflatable slides and wrote: "I just crash landed at SFO. Tail ripped off. Most everyone seems fine. I'm ok. Surreal..."
Anthony Castorani, who saw the flight crash land from a nearby hotel, told CNN. "You heard a pop and you immediately saw a large, brief fireball that came from underneath the aircraft. It began to cartwheel."
Weather conditions at the airport were reported as fine with a little wind.
The events leading to the crash remain unclear.
According to a report in the Daily Mail, Saturday's crash was almost identical to that of a BA Boeing 777 crash at London Heathrow five years ago.
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