Thieves have stolen about 40 brass memorial plaques from the Surrey and Sussex Crematorium.
Sussex Police said the plaques stolen from the crematorium in Balcombe Road, Crawley, had probably been sold to scrap metal dealers.
Insp Zahid Khan said: "Having a plaque stolen from a loved one's grave is clearly a distressing thing to happen."
He appealed for any scrap metal dealers who may have been offered the plaques to come forward with information.