NatWest branches in Selby and Tadcaster are set to close as the bank embarks on another round of closures.
Its taxpayer-backed parent, the troubled RBS group, is closing some 158 branches nationwide with more than 470 jobs now at risk.
The firm has blamed a surge in online and mobile transactions for the decline of the traditional banking over recent years. Transactions in bricks-and-mortar banks have fallen 43% since 2010.
Selby's mayor, Cllr Steve Shaw-Wright, told The Selebian, "This is a major loss to the economy of Selby Town, banking jobs are well paid with good prospects.
"I hope the staff in both [Selby and Tadcaster] can be relocated locally, I am also concerned what will happen to the premises, yet another coffee shop, bar or charity shop or just left empty?"
An RBS spokesperson said, "We interact with our customers over 20 times more through digital channels than physical ones. As customers change the way they bank with us, we must change the way we serve them
"The role of the branch is fast moving to a centre for advice, away from basic transactions. While the branch will still be a core part of our offering to customers, inevitably some branches will have to close."
The bank, 73% owned by the government, announced year-end losses of £7billion in February.