Pennsylvania State Police said the bus from Cumberland Valley Christian School in Chambersburg collided with a passenger vehicle on Interstate 81 at about 4:40 p.m. near Chambersburg.
All of the occupants of both vehicles were taken to hospitals.
State police said 17 adults and children were taken to Chambersburg Hospital, and six other patients were taken to Waynesboro Hospital.
Summit Health spokeswoman Jessica Walter gave slightly conflicting numbers of victims, saying 18 adults and children from ages 9 to 12 were taken to Chambersburg Hospital, and seven other patients were taken to Waynesboro Hospital.
Troopers and Walters said all were reported to be in stable condition and there were no life-threatening injuries. The injuries were described as "minor to moderate."
Trooper Tom Pinkerton said it was too soon to know if any charges would be filed.
"However, preliminarily, the driver of the Cadillac is the person that contributed to this crash," Pinkerton said.
He said the students had been traveling to Men-o-Lan Christian Camp in Quakertown, but the Chambersburg Public Opinion, citing a pastor associated with the school, said their destination was a church camp in Elizabethtown.
The state police said in a statement Sunday night that 79-year-old Edward Shaffer, of Hagerstown, Md., passed the bus on the left and took evasive action from an oncoming vehicle. Officials say he is believed to have over-corrected his vehicle, causing it to rotate sideways in front of the bus.
Troopers say the bus driven by 52-year-old Joseph Henderson, of Chambersburg, hit the passenger side of Shaffer's Cadillac. Shaffer's vehicle went into a ditch on the right side of the road. The bus partially entered the ditch, struck a guard rail and rolled onto its roof.
Three children and Shaffer had to be extricated from the vehicles.
Pastor Mike Sanders of the Open Door Church in Chambersburg said injuries appeared to include some broken bones, bumps and bruises.
"I'm just thankful that the extent of the injuries is what it was," Sanders told the newspaper.
Fire companies and ambulances from several stations responded and state police said other motorists helped remove passengers from the bus.
Vehicles on the heavily traveled interstate were detoured to the next exit.