The decision by AIB to remove cash services from 70 branches around the country - mainly in rural Ireland - amounts to the effective closure of the branches.
The Social Democrats say the move will disproportionately negatively impact rural and elderly people,
However AIB customers will now be able to conduct their cash banking from any post office around the country.
The Party's Finance Spokesperson Róisín Shortall says the move would have a significant impact on rural communities.
"A bank is a critical business within a rural community especially.
"Some of these towns that we're talking about that are losing cash services are not small towns by any means, many of them are thriving towns.
"The decision by AIB is just unbelievable."