Weather damage can cause headstones to become unstable and the age of some of the memorials can also be an issue.
Midlothian Council will carry out a survey to identify headstones that are no longer secure and pose a potential hazard to visitors, before notifying relatives and starting work.
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Hide AdWork has been completed at two cemeteries and will soon start at Newbattle Cemetery.
Councillor Wilma Chalmers, cabinet member for commercial operations, said: "We're making cemeteries more safe for those grieving for loved ones."