The pair had not been located by Monday night despite extensive inquiries with family and friends, and a search of floodwaters and the area has begun as a precaution, police say.
"We are out there looking for these men because we are concerned about their safety".
The town of Ingham, just north of Townsville, got over 10 centimetres of rain in just a few hours on Monday morning, according to the Bureau of Meteorology. It's feared the pair may have been swept into a drain.
Police had been called to the shopping centre on Ross River Rd half an hour before to reports of an attempted break in at Dan Murphy's.
The Port of Townsville remains open, but cargo loadings have faced interruptions due to heavy rain, a port spokeswoman said.
Hundreds have been rescued from their homes as floods continue to rise.
Below are some of the most striking images emerging from the disaster.
Townsville has been the hardest hit as heavy rainfall continues to flood far north Queensland.
A couple head home down a flooded street in Townsville.
Desperate residents had to contend not only with flash flooding, landslides and power blackouts, but also reptilian predators that have been spotted in residential roads and cul-de-sacs.
Just after 8pm last night, the spillway gates of the Ross River Dam opened and flash flooding warnings were sent out to many suburbs.
The government has said it will provide disaster relief for those affected by the floods, and encouraged people to apply for emergency assistant payments.
"We're getting food supplies in there".
"Anyone out there with a boat please go to ..."
On Saturday, as the flooding rapidly worsened, police in parts of Queensland were going door-to-door to warn residents to leave their homes.
She said the total damage bill was likely to cost "hundreds of millions of dollars because of the scale of it" in a long recovery.
"Our homes have been sacrificed to save the rest of Townsville".
Townsville Mayor Jenny Hill had described the rainfall as a "one-in-100-year event" and said Monday, "We're not out of the woods yet".
"Chris you are an awesome generous person thank you so much from the bottom of my heart".
They also had a warning for those venturing out into floodwaters on their own: "Crocodiles may be seen crossing roads, and when flooding recedes, crocodiles can turn up in unusual places such as farm dams or waterholes", says Queensland's Environment Minister Leeanne Enoch.
Two officers spent half an hour clinging to trees after their patrol vehicle was washed away in a "scary" incident while carrying out evacuations.
"It's a little bit scary because when it floods in Townsville, the crocs get into the water".