Waterford Council has been called on to take action over anti-social behaviour at Gallows Hill in Dungarvan.
The large man made mound dates from the 12th century and rose to prominence in recent years as part of the Adopt a Monument Scheme.
Various archaeological investigations have been carried out on site.
Fine Gael Councillor Damien Geoghegan raised concerns at the July Dungarvan/Lismore District meeting.
"Gallows Hill is a national monument and people like Eddie Cantwell and the Museum Society have done excellent work," he said.
"It's not acceptable that people are out there for hours on end on scramblers and motor bikes in a built up area. I ask that we take a look at closing off particular access points to the green area which has caused nothing but problems."
His comments were echoed by Fianna Fail's Tom Cronin who said he had also received many complaints in relation to scramblers and horses.
Dawn Wallace from the Council's Environment Department responded.
"I'm aware there are issues at Gallows Hill," she said. "People with scramblers and horses is a matter for the Gardaí but it has come to our attention on multiple occasions about dumping."
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