The 350 x 250mm engraved plaques were taken from the public plaque lawn, one of the older areas of the cemetery. They were found to be missing yesterday, though it is likely they were taken over the weekend.
Police believe the thieves may sell the plaques as scrap and will be speaking to local scrap metal and second-hand dealers.
City Council Cemeteries Manager Jeff Paris says where possible cemetery staff will contact the families concerned to let them know.
"It's a despicable and disrespectful thing to do and will be extremely upsetting to those families involved. We will be doing our best to contact them. However we may be unable to find the descendants of some of the deceased as the graves are so old.
"The only consolation is that last year cemetery staff photographed all the plaques and so we will be able to replicate the information on the plaques if they don't turn up."
Jeff says in older areas of the plaque lawn, the plaques sit flat on the ground, which makes them easier to lift. In the newer section staff have recently started fixing plaques on to concrete, which would make theft more difficult.
"It was quite random where they took them from - it wasn't from a line of graves but from all over."