It happened on the A5086 south of Cockermouth, in the early hours of Saturday morning.
Firefighters from Whitehaven were called to the scene at about 1.55am.
Inspector Chris Wright, of Cumbria police, said that the youngsters, who are all believed to be about 11 years old, were members of Wath Brow rugby club.
They are understood to have been returning to Wath Brow from a day trip.
Inspector Wright said: “The crash happened near Lamplugh, about four miles south of Cockermouth. There were about 50 children on board the coach, who were checked over by paramedics but none of them were injured.
“The driver of the bus was injured and may have suffered a fractured arm.”
He said that investigations as to the cause of the crash were ongoing, but initial speculation suggested the coach may have clipped a bridge.
In a statement released on its Facebook page yesterday, Wath Brow Hornets said: “Everyone at Wath Brow Hornets ARLFC is extremely relieved all under-11s coaches, parents and supporters are ok after the accident last night.
"Thank god you’re all safe and thanks to those on the bus who supported the kids through a very traumatic experience.”
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