Pictures posted on Twitter showed passengers jumping down the inflatable emergency slides and leaving the area, as plumes of smoke rise from the plane.
The cause of the crash is unclear.
Early indications suggest the plane came in too short and hit the seawall at the airport.
There were 291 passengers and 16 crew on board, Asiana said.
While the sequence of events remains unclear, it appeared the plane landed and then crashed on San Francisco International Airport’s Runway 28L, said Federal Aviation Administration spokeswoman Laura Brown.
Footage of the scene showed debris strewn on the runway and smoke pouring from the jet, as fire crews sprayed a white fire retardant into gaping holes in the craft’s roof.
One engine and the tail fin appeared to have broken away from the main wreckage.
Passenger David Eun 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…”
Mr Eun, who describes himself as a “digital media guy” and “frequent flier”, added: “Fire and rescue people all over the place. They’re evacuating the injured. Haven’t felt this way since 9/11.”
A witness to the crash, Ki Siadatan, said the plane “looked out of control” as it descended over San Francisco Bay to land just before 11:30 (18:30 GMT).
“We heard a ‘boom’ and saw the plane disappear into a cloud of dust and smoke,” he told the BBC. “There was then a second explosion.”
He saw events unfold from the balcony of his home in the Millbrae area of San Francisco, which overlooks the airport.
Weather conditions were fine and there was little wind, he added.
Arrivals and departures at the airport have been suspended since the incident……
6th July, 2013