There were 129 people on the Amtrak train, but no one on the train was injured.
Officials say two children, 6 and 9-year-old boys, were thrown from the vehicle and pronounced dead at the scene.
Their mother was transported to Duke Hospital. Authorities say her injuries do not appear to be life-threatening.
Police have not yet released the identities of the woman or her children.
Police say the SUV was on the tracks, when the railroad stop arms came down and it was apparently blocked in by traffic. Another car was stuck on the tracks, but it was able to get out.
"She was basically was stuck on the tracks while the train was coming," an eyewitness named Trae said. "Everybody was jumping out of their cars, running over there to assist her, to help her get out."
"I was just sitting there with my mouth open not even believing I had witnessed such a thing," eyewitness Tasha Colin said.
Those familiar with the intersection say it's common to see people stopped on the tracks.
"This is a problem we have going on every day in the mornings and afternoon," Trae said. "It's cars behind you and in front of you so you have nowhere to go."