Yellow warning signs put on gravestones labelled dangerous have been dubbed "disrespectful" and "hideous".
Plymouth City Council put up the signs on 197 graves at Efford Cemetery during a routine safety check.
BBC Radio Two presenter Jeremy Vine tweeted: "Covering the name of the dead person with a fluorescent warning sign is hideous."
The council said after "recent feedback" it would be "reviewing how these signs are displayed on graves".
Gravestones can topple. Children should not play in cemeteries for that reason. Very few people die from falling tombstones. This is not a serious safety issue. Covering the name of the dead person with a fluorescent warning sign is hideous.— Jeremy Vine (@theJeremyVine) November 7, 2018
The graves were marked during an inspection which the council makes every five years to keep its cemeteries in good order.
Inspectors found 197 of the 3,500 gravestones inspected were unsafe and could topple.
It placed warning signs on the gravestones and wrote to relatives of the dead whose graves were deemed dangerous.
Paul Ford, who found a warning sign on his grandparents' grave told Plymouth Live: "Where they have put the placard you cannot see who has been buried there; it looks more like a building site.
"I think it's disrespectful to cover up the names of the dead. If it was on the back it would be okay, but it's not.
"They should have made more effort not to cover up the names. It's an eyesore."
A Plymouth City Council spokesman said the owner of the grave was responsible for the memorial, and added: "If a memorial is found unsafe and/or in need of repair, we place a sign on the grave to advise the owner how to contact us to talk about options for repair and also to warn people and staff that it is potentially unstable.
"We also send a letter to the address we've got on record."