There are 15 complaints in the NHTSA database from drivers who say they heard a loud bang, and then sat through a downpour of glass.
One woman said she was driving home from getting her first oil change and tire rotation on the Veloster.
"All of the sudden there was a loud bang like a gunshot, and I heard something raining down on my car," reads the complaint, which is listed without any identifying information in the NHTSA database. "I looked in the mirror and saw glass flying everywhere... The glass was in my hair, down the back of my shirt and my pants."
All of the incidents happened on very new models, with less than 3,000 miles on the odometer. Two people said the roof exploded while the car was parked. One person was hosing the car down in the driveway when the glass shattered. This person said the glass flew as far as six feet away from the car.
Jim Trainor, a spokesman for Hyundai, said the company is working with NHTSA to look into the problem.
"Our evaluation is in the very early stages and Hyundai is in the process of examining each report," Trainor said. "As always, we will work closely with NHTSA on this evaluation."