A teenage girl who survived a plane crash in craggy, thickly-forested mountains of Washington state emerged from the wilderness after hiking "for a couple of days" and was picked up by a motorist who drove her to safety, authorities have said.

But the fate of Autumn Veatch's two step-grandparents, who were also on board, remained unclear.

Family members alerted authorities after the Beech A-35 failed to complete its flight from Kalispell, Montana, to Lynden, Washington, on Saturday afternoon.

Rescuers narrowed down a search area based on mobile phone data and typical flight patterns but there was no sign of the aircraft or its occupants until Autumn, 16, followed a trail to Highway 20, near the east entrance to North Cascades National Park.

A motorist picked her up and drove her 30 miles east to a general store in Mazama, where employees called emergency services. The Aero Methow Rescue Service sent a paramedic team to check her out before she was taken to a hospital in Brewster for treatment of what appeared to be minor injuries, said Cindy Button, director of services at the organisation.

"Our initial information is she sustained no life-threatening injuries and is somewhat dehydrated due to being out in the elements," said Scott Graham, chief executive officer of Three Rivers Hospital.

Okanogan County sheriff Frank Rogers said the girl had been "walking for a couple of days". He would not comment on the other two people aboard the plane, Leland and Sharon Bowman of Marion, Montana.

Serena Lockwood, manager at the Mazama Store, said the girl and a motorist came in, saying she had been in a plane crash. "She was obviously pretty traumatised," Ms Lockwood said.

Rescuers celebrated Autumn's survival, but immediately returned their focus to finding the wreckage, aided by her description of the crash site, said Lt Col Jeffrey Lustick, of the Civil Air Patrol.

"We're so happy about this," he said. "I've spent 30 years in the Civil Air Patrol and in search and rescue. Moments of joy like this can be hard to find."

Lt Col Lustick said he had spoken to Autumn's father, who said his daughter told him the plane crashed and caught fire after flying into a bank of clouds. She remained at the crash site for a day before deciding to hike down, eventually finding a trail and following it to the trailhead on Highway 20.

Five aircraft equipped with special radios for detecting the missing plane's emergency-locator transmitter have been searching the mountains, along with ground crews, officials said.

The plane crossed the Idaho-Washington border about 2.20pm local time on Saturday, but dropped off the radar near Omak, Washington, about an hour later. The last phone signal from one of the plane's occupants was detected at around 3.50pm.

Civil Air Patrol experts are analysing clues left by the phones that were on board.

"These grids contain some of the toughest mountainous terrain in the state," spokeswoman Julie DeBardelaben said.