Steven Van Lonkhuyzen, 37, and sons, Ethan, 7, and Timothy, 5, left their home at Lota, on Brisbane's bayside on December 11, intending to chart an inland trip to Cairns in time for Christmas.

A Queensland Police spokeswoman said the trio's Mitsubishi Pajero was found stranded in the Expedition National Park about 3pm Sunday.

She said a grazier noticed the car driving into the Central Queensland forest earlier in the week and went looking for it after media coverage surrounding the search for the trio intensified.

"Apparently the vehicle is bogged but they are all fine, safe and well, just a bit hungry," she said.

The national park is out of mobile phone reception range.

Police and local park rangers were en route to extricate the trio's vehicle.

The discovery came soon after police revealed they were planning to mount an air search for the family.

Fears were growing for the welfare of Mr Van Lonkhuyzen  and his sons after he was last seen filling his white Mitsubishi Pajero with fuel at a service station in Miles, 330 kilometres west of Brisbane, on December 11.

They had not been seen or heard from since.

Queensland police South West District Acting Superintendent Mick Bianchi said extensive ground searches had been undertaken in the past week in areas surrounding Miles, Taroom and Rolleston, with a particular focus on national parks.

He urged members of the public to aid police and emergency service in the search for the trio by checking remote camping areas, rest stops and roads, a plea that eventually led to them being found.

Heavy rainfall and storms closed many roads in central Queensland the weekend following the trio's departure, prompting minor flood warnings across many creeks and rivers.

Superintendent Bianchi  is expected to update the media later on Sunday.