Callous stone thieves have targeted monuments in Utley Cemetery.
Police and the public have condemned the heartless criminals, who were forced to abandon their haul before they could escape with it.
A local resident, who asked not to be identified, said he first spotted the damage when visiting the cemetery last Thursday.
He said he saw at least two headstones in the older part of the cemetery, near Skipton Road, which had been pushed over and broken.
“It makes you feel sick to know some mindless person would steal from a graveyard,” he added. “Those graves have been there for a very long time, and now someone has gone and done this to them.”
The incident has been condemned by Keighley Central councillors, whose ward includes the cemetery.
Abid Hussain said: “I’m really sorry to hear about this – it’s disgraceful.
“I hope the police enquiries are successful and they find those responsible. I feel for those whose loved ones’ graves have been affected.”
Khadim Hussain, who is also Lord Mayor of Bradford, called for security to be examined at the site.
“The office there was closed and is now empty – perhaps we should be looking at CCTV cameras in that area,” he said. “This is a very sad thing to happen.”
John Scholefield, Bradford Council bereavement and amenities manager, said: “There was some damage in Utley Cemetery caused by thieves, who attempted to make off with stone cut off some of the monuments.
“We think the thieves were disturbed because we later found the stone piled up before it could be removed. It is now stored in a safe place.
“We informed the police about the attempted theft, and we are in the process of trying to establish which graves had items stolen from them.
“If we identify any stone missing from a grave, we will contact the family and inform them.”
Inspector Di Collins, of the Keighley Neighbourhood Policing Team, said: "Criminal damage to tombstones and other memorials is something we take very seriously, particularly because of the distress it causes to relatives of the deceased.
"We would like to hear from anyone who might have witnessed this incident or who saw anything suspicious in the Skipton Road area between January 29 and 30.
“We would also be interested to hear from anyone who saw a dark red/purple hatchback in the cemetery on January 31.
"Anyone with information is asked to contact Keighley NPT on 101 or Crimestoppers on 0800 555111."