A Dunedin woman, who wished to be known only as Tracey, said during the past 18 months her daughter's grave at Dunedin Cemetery had been targeted at least 10 times.
Flowers, pots and mementoes had been stolen.
''It's so upsetting - it's disgusting,'' Tracey said.
''You put it up there to make yourself and anyone else who goes up there to visit a little bit happier about being there, so it's really sad.''
Aileen Ramsay, whose 2-day-old daughter died in 2011, said photographs on the headstone, which was shared with her father, had been smashed and a row of angels stolen.
As a result, she had stopped placing mementoes on the grave.
The attacks had made the grieving process more difficult.
The photograph was vandalised close to Christmas and the assailants were ''petty scum'', she said.
''It's only been about eight months and we've had something done to it twice.''
Tracey's daughter died suddenly in September 2013 shortly before her third birthday.
Since then, Tracey ''had about five different solar lights stolen, two pots, her little crystals, little butterfly-shaped things and bunches of flowers''.
The most recent theft occurred about three weeks ago and, in the most upsetting incident, two pots were taken shortly before Christmas last year, she said.
A headstone would be installed in the coming months and Tracey was anxious about it.
''It's a wee bit different, so I'm a wee bit worried it's going to be vandalised.''
She was unsure if it was thieves preying on an easy target, vandals or children who did not know any better, but the effect was the same regardless.
''They are scumbags.''
She had contacted police and the Dunedin City Council about the issue and police were investigating.
The pair hoped the council would tighten security at the cemetery and that CCTV could be installed.
Council parks manager Lisa Wheeler said the council had received about a dozen complaints about vandalism and thefts at the cemetery, but ''we haven't had any complaints over the last couple of weeks''.
All complaints had been referred to police and they had been more actively patrolling the area as a result, she said.
Council security guards, who patrolled Brighton looking for freedom campers, were also checking in on the cemetery in a bid to deter thieves.
The council had no plans to install CCTV, although ''we will have to look at it and see if we can do something'', Ms Wheeler said.
''The headstones are private property so we can't do too much more than try to keep them secure.
''But it is a public area and unfortunately people will sometimes do this mindless stuff.''
