Officers are mounting extra patrols to try and prevent future damage to Hambleton Hough west of Selby.
It is forbidden to use bikes in the reserve and police say there are several signs telling visitors about that.
But now police have been told of people using bikes in the woods and damaging the area.
“A lot of the tracks within the woods have had damage caused to them as they have been dug up and made into jumps for bikers to use,” said a North Yorkshire Police spokesman.
“The land owners are having to spend a lot of time and money to get the tracks back to how they were, to ensure that the bridleways are safe to use again.
“Police will be patrolling the area and will take action if any persons are caught causing damage to the land.”
Police urge anyone using the reserve to treat it with respect and not have bikes in any part of the wood.
