An Amber Alert has been issued for the boys, and police say they also are looking for Scott Chandler, who owns the facility, the Albuquerque Journal reported Saturday.
State police said they believed the teenagers, ages 13-17, were in danger because of "the nature of this abduction."
The search was focused on a remote area in the 30,000-acre Tierra Blanca Ranch High Country Youth Program near Hillsboro, and the Deming area along Interstate 10.
State police and child protection workers raided the ranch Friday with court orders to take custody of the boys. The headquarters were empty except for a ranch hand.
Gov. Susana Martinez said officials were concerned the boys had been moved to keep them away from investigators.
The state Children, Youth and Families Department claims in court documents to have evidence of pervasive medical neglect, systematic emotional and psychological abuse, the shackling and handcuffing of children and possible criminal sexual contact.
Chandler and his attorney, Pete Domenici Jr., have denied the charges.
In a statement Friday, Domenici said the youths were safe and on a 'previously scheduled activity." He said they would be turned over to their parents, although he did not say when.
Despite Domenici's assurances, state police Sgt. Emmanuel Gutierrez said, "this is still an active investigation," CNN reported.
"We have allegations of abuse," Martinez said. "We're required by law to investigate, and when you suddenly show up to the place and everybody's gone, it's of huge concern to us."