They have been unable to use their cards at ATMs and also in store to pay for goods.
One angry Ulster Bank customer told Belfast Daily: “I think this the end of the road for me and Ulster Bank.
“They have had enough chances to sort this whole mess out. And it keeps happening. Well, that’s me finished with them.”
The problem is not only affecting Northern Ireland, but also NatWest and parent company Royal Bank of Scotland (RBS) customers.
In a short statement, issued on Monday night, RBS said: “We apologise to customers for the inconvenience caused.”
It is now the fourth time in the past year that customers have unable to use their cards because of computer problems.
In March, Ulster Bank customers faced a fresh technical glitch to their accounts.
A problem was preventing customers from accessing their mobile banking accounts.
However, the bank later said it had fixed the issues and said no other services have been affected.
It apologised to those users who could not log in to the mobile banking application.
Ulster Bank at the time: “We were aware of a technical problem this morning which prevented customers from logging in to our mobile banking application. This has now been resolved.”
RBS and Natwest customers had also been experiencing similar problems.
Earlier this month a technical glitch meant customers couldn’t access their accounts at ATM machines.
Last year Ulster Bank revealed it paid out over £18m to almost 300,000 Northern Irish customers after a technical fault left them without proper access to their bank accounts for weeks over the summer.
The bank plans to close seven branches and four sub-offices in Northern Ireland by this June.
RBS now has permanent staff at the Ulster Bank in Belfast as it attempts to overcome problems.