The National Weather Service reports the area has received more than 6 inches of rain since Saturday.
Officials had no immediate reports of anyone hurt or significant damage. Part of the roof of a convenience store in Sugar Land collapsed.
CenterPoint Energy had about 6,900 homes and businesses still without electricity this afternoon as crews worked to restore power. Nearly 45,000 customers had lost electricity Saturday night.
The Houston Fire Department answered about 150 vehicle rescue calls from 5 p.m. to 10 p.m. Saturday as water flooded roadways.
Forecasters say Montgomery County, just north of Houston, had some hail the size of golf balls.
