More than 400 schools and colleges across the country are reported to have received emails claiming a device has been planted and demanding cash.
Humberside Police said 19 schools in East Yorkshire and North Lincolnshire had received the email.
Detective Superintendent Tony Cockerill said: “We have been liaising with our counter terrorism colleagues across the country and it is not believed that the threats are credible.
“We have spoken to all schools who have contacted us, reassured them that there is no need to evacuate and offered them security advice.”
A North Yorkshire Police spokesman said it had also had a number of reports about the bomb hoax.
He said: "Our Cybercrime Unit detectives, supported by local officers, have looked at these incidents and it is not believed there is any genuine threat.
"We are working with schools to offer reassurance and address any concerns."