The statue in Monk Bretton was damaged at some pointÂ between Tuesday,Â July 24 and Thursday, August 2.
Glass panes on theÂ monument, which commemoratesÂ the local glass industry, were smashed.
CRIME: Sheffield murder suspect still on the run The incident was reported toÂ the police by a local councillor and an officer from the Cudworth Neighbourhood Team, PC Sam Whitehead, began investigating and found CCTV footage capturing two 12-year-old boys throwing stones at the statue.
They were identified, interviewed and admitted causing the damage.
They are to be dealt with byÂ Barnsley'sÂ Youth Offending Team.
PC Sam Whitehead said: 'This monument means a lot to the local community and I'm pleased that the two boys admitted the damage they had caused and apologised for their actions.'