Hot drinks will continue to be served at meetings but people are asked to bring their own reusable cup to use.
If all area boards do make this pledge then this could potentially save around 3,240 plastic cups going to landfill each year, based on 30 cups being used per area board meeting.
John Thomson, chairman of Malmesbury Area Board, said: “This is a relatively simple thing to do but should have a positive impact.
“If we all do our bit and make simple changes such as this then it will contribute to reducing plastic pollution of our planet.”
A spokesperson for Malmesbury Against Plastic said: “This work has shown the power of individual action. If people need convincing their actions won't have an impact, take a look at this example. Any action or habit change, no matter how large or small, will have a significant impact on the health of our planet."