Parents are being asked to ensure their children do not play in York Cemetery after hours.
Warden Bill Shaw says there have been a growing number of incidents of youngsters climbing over walls and fences to get into the cemetery, and then vandalising equipment.
"The cemetery is not a playground and has inherent dangers for anyone who strays off the paths," he writes in a letter distributed to local houses.
"There have been two serious vandal attacks on builders' plant in the last month between 5.15pm and 7.30pm, when the windows of a machine have been smashed."
The charitable trust that looked after the cemetery could ill afford the extra costs of such vandalism, he said.
Police had been informed and had asked to be told immediately if there were any further incidents, so they could come along and deal with the intruders.
Mr Shaw appealed for parents not to let their children come in the cemetery after 4.30pm, and also asked residents to call police if they saw young people in the site after this time.
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