Fourteen - seven of them in Scottish locations - are classed as the last bank in town, sparking claims the move is a "stealth attack on local communities".
Areas from the Borders to the far north of Caithness are affected, with closures beginning in May. Most of the branches are being replaced by a mobile banking van service.
The bank has defended its decision, saying there has been a 30% drop in branch transactions since 2010 and more customers are banking online and via the telephone.
However, unions and consumer campaigners expressed anger over the closures and called on the bank, which is 80% publicly owned, to think again.
Unite national officer Rob MacGregor said there had been no proper consultation. He said: "This is a stealth attack on local communities by bailed-out RBS.
"Taxpayers have a right to be angry that RBS has quietly embarked on a major programme of branch closures. While RBS senior executives get millions of pounds in payouts, there are communities up and down the country being denied access to a local bank. George Osborne, whose own constituency is affected, should intervene and demand that RBS rethinks these decisions."
One of the "last banks in town" is in Castletown in the north of Caithness, where the Norfrost refrigerator factory closed last year with the loss of 70 jobs.
Brenda Herrick, chairwoman of Castletown Community Council, said the population had already dropped from 798 to 620 between 2001 and 2011 and residents would feel the impact of the bank's closure. "It is just another thing we are losing here in Castletown. It will make life a little more difficult," she said.
Caithness, Sutherland and Ross SNP MSP Rob Gibson said: "I will be contacting RBS to find out how they came to this decision and what support will be offered to the staff at the Castletown branch.
"It is clear that some people's banking habits are changing. However I would like to know why RBS are deciding to pick on people in a remote and rural area who do not have access to the fastest broadband speeds."
At the other end other country, Tory MSP John Lamont, for Ettrick, Roxburgh and Berwickshire, is seeking a meeting with the bank about the closure of three branches - Chirnside, Greenlaw and Newton St Boswell - that he believes will adversely affect local customers.
Patthead, East Linton, Longniddry and Bonnybridge are to lose their only bank, and Dundee and Paisley branches will also close.
A spokesman for RBS said: "Banking has changed significantly over the last few years as more and more of our customers are banking with us where and when it is convenient for them.
"We have to adapt to what our customers want, which is why we're investing in a range of other ways our customers can bank with us, including online and telephone banking, our mobile app, and in any one of the Post Office's 11,500 branches across the UK."
RBS said it had been telling affected customers about the closures over the past two months, having announced in February it planned to cut costs by more than £5 billion over three to four years.