Last year, Glasgow City Council was approached by the Scottish Prison Service about the possibility of finding work for offenders nearing the end of their sentences.
In March, a team of three was put to work in Cardonald Cemetery after being given training - including on health and safety issues, processes for inspecting memorials and ways to make them safe.
A report from Brian Devlin, the council's land and environment boss, said: "At that time, there was a limited inspection and maintenance programme for memorial safety within council cemeteries."
Over the years, the public has raised a significant number of concerns about the condition of memorials in cemeteries.
Mr Devlin said: "Most of the 'making safe' of memorials is provided by sinking the memorials into the ground upright in the area where they would normally be placed. In most cases, this is provided to ensure the inscription is visible."
After spending two weeks in Cardonald Cemetery helping with site clearance, the prisoners began memorial inspection work in the Eastern Necropolis.
Mr Devlin said: "To date, the team has dealt with more than 300 memorials which has improved access and assists in ground maintenance operations.
"Given the success of the programme, the senior management at the Scottish Prison Service Barlinnie are seeking agreement from the city council to continue with the pilot."
In addition to the work by the prisoners, offenders issued with payback orders have helped install paths in the Western Necropolis and are painting the gates at Riddrie Park Cemetery.
Council spokesman Alistair Watson said: "The pilot has been a success with almost 400 memorials repaired or reinstated so far.
"It has shown a number of benefits such as preparing prisoners for life back in their communities."