The force's control room took 487 emergency 999 calls in the 24-hour period from 7am on Saturday (July 7) and 7am on Sunday.
It is among the highest number of calls the force has ever seen, placing huge demand on resources.
North Yorkshire Police said Numbers of 999 calls usually average between 200 and 300 a day, depending upon the time of year.
Non-emergency calls to 101 usually average between 500 and 650 a day and on Saturday the force took 729.
Chief Inspector Charlotte Bloxham, head of the force control room, said: “The summer is always a busy time for us however with the recent high temperatures and events such as local race meetings, concerts and the World Cup, we have seen increasingly high demand placed upon the force. This picture is replicated for forces up and down the country.
“We want to see our communities embracing the glorious weather and enjoying the events taking place across the county in the next few weeks, however we must ask that people enjoy themselves responsibly.
“Most revellers in towns and cities enjoy a few drinks in the sun, including football fans who have relished the on going success of England during this World Cup tournament, and return home without any issues.
“There are a small few, however, that ruin it for many by becoming aggressive or violent after too much to drink. We want to convey a clear message that we will continue to work around the clock to keep people safe and those who cause alarm or harm to others will be removed from the streets.”
The significant demand is set to continue this week, with a number of annual events taking place such as the Great Yorkshire Show, Seamer Fair, and York Races.