Sheffield Council has urged residents to be patient while it completes work to tidy up a graveyard.
The authority says a number of headstones in Crookes Cemetery are unsafe and need to be laid flat.
It has been carrying out the work for several months, with the aim of soiling and reseeding the area to make the area a safer and nicer place for people to visit.
But some relatives of people buried in the cemetery say the work has left it looking a mess.
Ian Betts, from Fulwood, regularly visits the graves of his father and grandparents, and says he plans to end up there himself one day.
But he is becoming 'increasingly dismayed' by the state of the cemetery.
Mr Betts said: "On each visit, more and more of these acts have been carried out leaving a field of apparent vandalisation.
"I can understand that the council has responsibilities with regard to public safety but the manner in which the work is carried out is appalling.
"There are large areas that now look as though a battle has taken place."
Mr Betts said headstones had been damaged and not all were laid face up with the engraving showing. He said the stone next to his grandparents' had been laid over their grave.
"Surely the dead are entitled to some degree of respect," he said.
The council apologised for any concerns Mr Betts and others had about the work - and said it had not yet had any complaints.
Cabinet member for culture, parks and leisure Mary Lea said:
“Over the last few months, we have been carrying out a programme of the removal of dilapidated memorials, as there are a high number that have fallen into disrepair.
"Where possible, we will leave the headstone upright but, if this is loose, we will lay the headstone flat on the ground with the inscription showing. The headstones are laid on the graves that they were on originally, and are not moved onto other graves.
“Unfortunately, the area where we work will not look its best until we have finished, and soiled and seeded the area.
"We hope that people will understand the need for these safety works to be carried out, and would like to reassure them that all works are being carried out in a respectful and sensitive way, to ensure that the cemetery is safe, tidy and fit for purpose in the coming years.”