At 10:26 p.m., doppler radar indicated a line of severe thunderstorms had formed and it was moving east at 40 mph, according to the National Weather Service.
The storm is capable of producing cloud-to-ground lightning and people outdoors should seek shelter immediately.
The storms are along a line extending from Point Breeze to six miles east of Darien or along a line extending from 11 miles north of Albion to nine miles southwest of Batavia.
The storm is capable of producing damaging winds up to 60 mph and potentially damaging hail.
"These are dangerous storms," the weather service warns. "If you are in the path, prepare immediately for damaging winds, destructive hail and deadly cloud-to-ground lightening."
If indoors, the weather service warns people to stay away from windows.
The warning is effect until 11:45 p.m., a thunderstorm watch remains in effect until 1 a.m.
UPDATE 10:57 p.m.: The fast moving storm has passed through southern Genesee County and the warning for southern Genesee County is cancelled.
UPDATE 11:05 p.m.: The warning is now cancelled for all of Genesee County. A watch remains in effect until 1 a.m.