Stephen Foster, emergency-management director for Woods County, Okla., was racing along county roads last Saturday to keep an eye on a storm that was spitting out tornadoes when he ran into an unexpected problem: a two-mile-long line of traffic.

"It was like a football game getting out," he said. "Everybody was trying to film the storm. That just really slows down our emergency vehicles. We can't get where we need to go."

Officials in storm-ravaged parts of Oklahoma and Kansas are complaining about last weekend's influx of storm chasers—a ragtag band of amateur weather spotters, researchers, extreme-weather tour guides, news crews and adventure seekers. Their ranks have expanded in recent years with the advent of TV shows such as "Storm Chasers," cheaper technology for tracking weather and social-media sites where people can post news and videos of the latest storm.

Now, when a well-publicized storm pattern like last weekend's rolls around, chances are high for what storm chasers call "a convergence," in which they begin to get in each other's way—not to mention the way of emergency workers.

"In the past, there might have been 25 or 50" storm chasers during a weather event, said Todd Thorn of Storm Chasing Adventure Tours of Bozeman, Mont., which charges clients $2,400 for a week of chasing. "Now, there might be several hundred on a big day on the weekend."