Many roads are closed because of high water and debris, preventing rescue crews from reaching the stranded.
Up to 7in of rain fell in three hours in the Boulder area on Thursday morning, the third day of rain.
Residents in two areas south-east of the town of Estes Park have been ordered to evacuate after an earthen dam gave way in the area.
Further heavy rainfall is expected on Thursday.
Emergency officials have reported three deaths: one in Colorado Springs; one when a structure collapsed in Jamestown; and another in Boulder.
A 20ft wall of water was reported in Left Hand Canyon, north of Boulder, according to National Weather Service meteorologist Bob Kleyla.
Rescuers in the area were trying to get through debris to reach a firefighter who climbed a tree to escape the water, according to US media reports.
Some 400 students at University of Colorado, Boulder, were evacuated and classes were cancelled on Thursday because of the flooding.
Mandatory evacuations have also been ordered for the Jamestown and Fourmile areas.
Colorado State Patrol Captain John Burt said damage was being reported across several counties, including Boulder, Larimer and Jefferson, north-west of Denver, and El Paso County around Colorado Springs.
Almost all roads to Boulder had been blocked or flooded, according to the Denver Post.
Standing water on a road caused some traffic delays into Denver International Airport, but not to flights.
Officials told NBC that water reached as high as first-floor windows in some parts of Boulder, while cars were seen floating in the streets.
An emergency bulletin from Adams County, east of Denver, warned residents: “Stay away or be swept away.”
Boulder emergency management spokeswoman Gabrielle Boerkircher told AFP news agency the rainfall had been unusual not only for the amount of rain but for how the storm was behaving.
“It’s been a weird storm,” she said, adding it had been “turning back around on itself all night”.
Vr5vpPD8N5UImage source: Wikimedia Commons President-elect Donald Trump celebrated his election victory at the Ultimate Fighting…
Millions of voters across the US chose to return Donald Trump to the White House…
Donald Trump declares victory in the US election as he addresses jubilant supporters in Florida.…
Stocks around the world are rising as Donald Trump appears to be on the cusp…
Donald Trump has won Pennsylvania, North Carolina and Georgia and taken a lead over Kamala…
Quincy Jones, the celebrated musician and producer who worked with Michael Jackson, Frank Sinatra, Ray…