A Brisbane father and two boys have been found safe and well after spending days bogged and hungry in a national park in outback Queensland.

Steven Van Lonkhuyzen, 37, and his two sons, seven-year-old Ethan and five-year-old Timothy, were found by a local grazier on Sunday afternoon in Expedition National Park, north-west of Taroom in the state's central inland.

Police said the farmer saw their vehicle enter the park a few days ago and was alerted to their disappearance after media reports.

Police were on their way to the national park where the grazier was assisting the family.

The trio left their home at Lota on Brisbane's bayside for Cairns on December 11.

They were due to arrive in Cairns on December 15 but they had not made contact with family or friends.

Authorities said they became stranded in the national park after their four-wheel-drive vehicle became bogged.

Police said it was out of character for Steven Van Lonkhuyzen not to be in contact with family. ( Supplied: QPS )

A police spokesperson said the trio were "very hungry".

Acting Superintendent Mick Bianchi said earlier on Sunday that police had conducted extensive searches over several hundred thousand square kilometres over the last several days, including areas of Miles and Taroom, through to Rolleston, and in particular national parks.

Mr Bianchi said the efforts of police and farmers in the search highlighted community spirit.

"Police from all 60 divisions in the South West District have been involved to varying degrees in this search," he said.

"We've had farmers and graziers searching their properties, local store owners checking to see if they had passed by or dropped in, mining companies and mustering helicopters checking lands, as well as park rangers searching parks and camp sites.

"We are all very thankful that we have a happy outcome."

Police said on Saturday the trio could be stranded after recent heavy rains in the area caused localised flooding.