"One vehicle left the roadway and rolled several times into a paddock, and a second vehicle tipped onto its side attempting to avoid the first vehicle," New South Wales state police said in a statement after launching a crash investigation.

"The vehicles did not collide with each other."

Police, emergency services and troops removed all 32 occupants of the two trucks in Saturday's incident near the flood-prone New South Wales city of Lismore.

All of the occupants were assessed medically but only 13 of them required treatment in hospital, state police and the federal government said.

Police said the injuries "appear to be non-life threatening".

Prime Minister Anthony Albanese told a news conference that six of the soldiers had been seriously hurt.

"These men and women are heroes who were on their way to help people in need," he said.

Initial figures provided by emergency services had put the number of patients following the accident at 36.

Australian Defence Force personnel have been deployed to help cope with the impact of ex-tropical cyclone Alfred, which has lashed a swathe of the eastern coast with heavy rain and powerful winds.