BBC NEWS — A torrent of mud fell on to the BR-376 highway in the state of Paraná, hitting more than 21 vehicles, authorities said.
Rescue workers at the scene said bad weather and the remote location were complicating the search effort.
Firefighters are using a thermal camera to locate possible survivors. Up to 30 people are thought to still be missing.
Aerial footage shows one lorry precariously hanging over the side of a bridge. Rescue workers found the body of its driver, who was identified as 62-year-old João Pires.
A relative said he had worked as a lorry driver for most of his life and was well acquainted with the road where the accident happened.
The name of the second victim has not yet been released.
Another lorry driver whose cab was buried in the mud was rescued with only minor injuries. José Altair Biscaia, 43, recorded a video of himself on his phone as he was trapped.
"I'm alive, thank God. I'm in the middle of the mud, just in a little corner which is left of the lorry. I'm full of cuts. but I'm alive," he can be heard saying in the footage.
The inside of his cab looks mangled and there are blood stains. Outside the window there appears to be a wall of solid mud.
So far, six survivors have been located.