The accident occurred Tuesday night along U.S. 83, The (McAllen) Monitor reported. The report said one person was arrested and three others fled the scene.
The Border Patrol said agents had tried to stop the van but it took off and "flipped" over as it headed east. Officials said they suspect the van's occupants were illegal immigrants because the driver tried to evade authorities, The Monitor reported.
Palmview police Cmdr. Lenny Sanchez said it was "real hard" to determine the ages and genders of the dead "due to their faces being severely bruised up."
Dianna Castillo, 23, who lives near the scene, said bodies "were everywhere."
"I wanted to cry because it's really sad because they came over here to live a better life and then they lost their lives," she said.