Almost half of the headstones assessed so far in a Fife-wide safety review have failed.
Around 10,000 memorials in Fife graveyards have been checked, with a failure rate of between 45% and 50%.
The review was prompted by the death of an eight-year-old child, crushed in a Glasgow graveyard in 2015 and an incident in Inverkeithing Cemetery the following year during which a headstone collapsed and a child suffered a broken arm.
Fife Council launched a survey of the 100,000 headstones across its 115 cemeteries to establish their condition.
So far, around 10% have been checked in cemeteries where memorials were deemed to pose the greatest risk.
Some £300,000 a year has been set aside to repair those found to be in a hazardous condition.
Tay Bridgehead Liberal Democrat councillor Tim Brett joined the teams tasked with the memorial inspection programme which began around 18 months ago.
He said: “This is a massive task to check that all of these headstones are safe but I was interested to see the work that is being done.
“Two small squads of staff are tackling this issue by carrying out inspections to all headstones and this allows the staff to record information about the headstones which can then be used to monitor progress and schedule future re-inspection.
“A significant number of headstones, particularly in the older part of cemeteries, need to be made safe and the squads are doing this as they go.
“At this stage it is difficult to say how long it is likely to be before all headstones are inspected, but I was pleased to have the opportunity of seeing this at first hand.
“I will continue to check with the bereavement services team with regard to progress.”
Senior manager Alan Paul said: “We have an ongoing survey and headstone remedial programme to make sure our cemeteries remain safe to all who use them.
“We will continue to roll this out across Fife.”