The Welshpool branch will close first, on September 16, with the Newtown branch following on September 23.
Local politicians say that its is another blow to local communities.
The area's MP Craig Williams, is concerned and disappointment over Barclays’ plans to close the branches and wants urgent assurances that its banking services will be protected for its customers.
He said: “I am today incredibly disappointed to learn of Barclays’ plans to close its branches in Newtown and Welshpool. This decision will mean that Barclays will now have no physical footprint in Montgomeryshire, which is an enormous blow to staff and customers of both branches, as well as the constituency as a whole.
“Whilst I accept that the number of in branch banking transactions has fallen significantly over the past few years, over the counter services are of vital importance to customers who prefer not to bank online, or who are unable to – particularly in rural areas such as Montgomeryshire. The facility to use the Post Office for some banking services does not fully compensate for the closure of a personalised and local branch.
“I am seeking an urgent meeting with Barclays’ representatives to discuss how it plans to provide services for its disenfranchised customers, and to ensure that continuing to provide personal and tailored services for those without access to online banking is its top priority.”
Barclays said the decision had been taken due to a sustained fall of in branch customer transactions.
Montgomeryshire member of the Welsh Parliament Russell George has said that while banks have pointed out the use of online banking, there remains a strong need for the presence of high street banks.
Mr George said: "I am extremely disappointed to hear of the closure of Barclays banks within Montgomeryshire and I will be querying the data provided in their reasoning for closing the banks, as I know that many people use both banks.''
''Whilst banks have pointed out the use of online banking there remains a strong need for the presence of high street banks.”
''Another bank branch closure will not only have a detrimental impact on the bank's loyal staff and customers, especially those who are elderly and vulnerable, but it will also have implications for the local business community, for Welshpool and Newtown as towns and the wider area, and for the reputation of Barclays.''