An investigation has been launched after a number of trees and plants were damaged at the Old Mine Nature Park.
Police say the area, near New Edinburgh Road in Fallside, also appears to have been used for camping, with evidence of fires being set.
The wood, which is run by the Forestry Commission Scotland, was officially opened in June 2013, with many areas still under development.
It would appear that a number of trees - some still with plastic tubes around the trunks - were deliberately damaged sometime between noon on Friday, March 20, and 3pm on Sunday, March 22.
Police have also received reports of damage caused by fires.
A spokesman said: “It would appear that there is evidence of camping in the area with fires being wilfully set and litter lying all around.
“This area has become popular with dog walkers, and I would encourage them to report anything suspicious.”
The Forestry Commission said it was working with Police Scotland in a bid to curb anti-social behaviour at the site.
Stuart Chalmers, of the commission’s team in the area, said: “We have seen damage to some larger birch trees and a few smaller trees and although it was fairly minimal, it’s never the less it is disappointing.
“Old Mine Park is a special place and a fantastic resource for local people and we want to keep it that way.
“We’re working with the local police to help nip this antisocial behaviour in the bud.
“We want everyone to help us look after the site to keep this amazing green space looking good.”
Paul Devlin, head of prevention and protection in North Lanarkshire for the Scottish Fire and Rescue Service, added: “Setting fire to refuse or grassland is dangerous, criminal behaviour that really does puts lives at risk.
“The fact is any fire is out of control as soon as it starts.
“Many deliberate fires are caused by young people so we need parents to make sure their teenagers know that setting fires could cause a tragedy.”
Anyone with information regarding the incidents at the Old Mine Park is urged to call Police Scotland on 101. Alternatively, call Crimestoppers on 0800 555 111.