They'd been specially provided to mark the 75th anniversary of D-Day.
Police have described vandalism at a number of military gravestones in Shipley as a 'mindless act of destruction'.
It happened between 11am on Monday 3 June and Tuesday 4 June at Hirst Wood burial ground.
The gravestones had been specially provided by the Commonwealth Graves Commission in remembrance on the 75th D-Day anniversary.
Detective Inspector Amanda Middleton, said:
“Our investigation is ongoing into the vandalism of these gravestones. The gravestones were destroyed in what was a mindless act of destruction and I would urge anyone with any information to come forward and speak to the police.
“High visibility reassurance patrols have been stepped up in the area whilst officers continue with their enquiries.”
Anyone who witnessed this incident or has any information is asked to contact Bradford District Police via 101 quoting log number 952 of 6 June.
Information can also be passed to independent charity Crimestoppers on 0800 555 111.