English Heritage is working with the police after three separate incidents of illegal metal detecting in as many months at the Whitby Abbey site.
Since March, 14 holes have been dug across the site while the property is closed at night.
It is also known as “nighthawking” and is a form of theft.
Whitby Abbey has been the subject of numerous archaeological digs over the years and there is nothing to suggest there are further remains to be discovered on the site.
Clea Warner, English Heritage Area Manager for Yorkshire, said: “This illegal activity is deeply disheartening. Whitby Abbey is a precious historic place and people who choose to damage it are robbing everyone of our collective heritage. While it is extremely unlikely anything significant remains in the ground, if these people have found something and not declared it they are denying us all further knowledge of Whitby.”