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”.
Vr5vpPD8N5UMisleading allegations, rumours and outright lies about voting and fraud are flooding online spaces in…
At least 158 people have died in Spain's worst flooding disaster in generations. On October…
Google has been fined two undecillion (a two followed by 36 zeroes) roubles by a…
Embarking on a home remodel is an exciting journey, promising enhanced comfort, increased property value,…
The US presidential candidates continued to campaign across key swing states on October 20. Footage…
Elon Musk has said he will give away $1 million a day to a registered…