Damage was caused to two plaques at the Memorial Gardens in Carrickfergus beside the main Cenotaph recently.
This is one of the incidents of vandalism that police are investigating in Carrickfergus.
Other incidents include graffiti and damage to bus shelters.
Police are working with Mid and East Antrim Borough Council and the Policing and Community Safety Partnership to address a number of concerns regarding anti-social behaviour and vandalism in the Carrickfergus area.
Neighbourhood Inspector Colin Ash said the increasing nature of these reports is concerning and causing distress and inconvenience to local residents.
“There is no excuse for the mindless vandalism that has taken place and we are appealing for those involved to stop and think about the damage they are causing to their own community.
“The Neighbourhood Team is focusing on this issue and would encourage anyone with information about those involved to contact us on 101,” he added.
Mayor of Mid and East Antrim, Councillor William McCaughey, condemned the recent vandalism.
“To vandalise plaques in the memorial gardens in this way is just reprehensible. I would encourage anyone who has any information on these incidents to share that with the PSNI without delay,” he added.