They are Travis, Williamson, Bastrop, Llano, Burnet, Colorado, Fayette, Hood, Jim Wells, Kerr, Kimble, La Salle, Live Oak, Mason, McMullen, Nueces, Real and San Patricio.
Residents were evacuated from homes Tuesday in Kingsland and in nearby Marble Falls, which was being overwhelmed by the Colorado River.
A flash flood warning was in effect for Llano, Fredericksburg and Kingsland until 3:30 p.m. local time.
A few miles away, in Kingsland, the swollen river rushed against the top of the RM 2900 bridge for hours, eventually causing it to collapse, video from CNN affiliate KEYE showed. Major flood stage is 23 feet (7 meters); it's not expected to drop below major flood stage until Wednesday.
The Llano County Office of Emergency Management says people trying to go around barricades is one of their biggest concerns as the water continues to rise along the Llano River.
Texas Parks and Wildlife says state game wardens have already conducted several air and water rescues along the Llano River.
Torrential rain has fallen across central Texas for two days with Llano County being deluged by 30.5cm (12 inches) of water.
MS toddler found stabbed and dead in oven
Williams said he won't release the names of the grandmother or the toddler until the filing of the murder charge is completed. A woman in Greenville, about 20 miles from Shaw, pleaded guilty to killing her 3-year-old son in an oven in March 2011.
Gov. Abbott released a statement urging 'all Texans to take their safety into their own hands by closely monitoring changing weather conditions and heeding warnings from local officials'.
Water from the Colorado River pours over the Max Starcke Dam on Tuesday. The National Weather Service warns that, while the river is believed to have peaked as of early Tuesday afternoon, a second crest is expected Wednesday morning.
Four people were washed away last week when the South Llano River, which becomes the Llano River downstream, overran an RV park in Junction, Texas. The bodies of three men were recovered and on Tuesday morning, one remained missing.
The rain also was causing problems in other parts of Texas.
Flooding has closed numerous roads in the area.
Unfortunately for the water-logged region, additional rainfall is expected in the coming days, as the prevailing flow from the Gulf of Mexico gets a shot of additional tropical moisture from the remnants of Tropical Storm Rosa, which is expected to sweep into the area late this week.