Two branches of RBS in Angus and the Mearns are to close in November.
The bank said it had taken the “difficult decision” to shut its outlets at Swan Street, Brechin and in Laurencekirk High Street on November 4.
Brechin councillor Bob Myles said he was “very disappointed” at the decision.
The bank is suggesting that people can use near-by post offices to check their balance, deposit and withdraw funds. There will also be a mobile branch service which will visit both towns after the closure.
The news follows the closure of the RBS branch in Kirriemuir earlier this year.
RBS said the number of transactions which take place at both branch had dropped by 24% since 2011 and that fewer than 50 people used each location on a weekly basis.
Mr Myles said: “As an RBS customer myself I’m very disappointed that they have taken that stance.
“I’m sure they have a lot of customers in Brechin. The service at the branch has always been excellent.
“I know that people of my vintage like to be able to go into a bank and speak to somebody face to face rather than trust doing things over the internet.”
A spokesperson for RBS said they would be writing to customers about the closures and also displaying posters in the branch.
She added: “Our customers are increasingly using alternative ways to bank with them such as online and mobile banking.
“As a result, branch transactions have declined by around 36% since 2010 whilst online and mobile transactions have grown by more than 300%.
“Between now and the closure date, we will engage with all of our customers, local businesses and the wider local community to make sure they are aware of the alternative ways of accessing their banking with us in the local area, and to answer any questions they might have.”