ANZ says business will continue as usual today, despite dozens of workers going on strike.
The industrial action comes as First Union members demand a 5 per cent pay rise.
ANZ says the strike is an attempt by the union to disrupt the bank in any way it can.
However, a bank spokesperson said all branches would remain open and bank services would be available today.
ANZ said about 110 people - or less than ten percent of the unionised staff - didn't turn out for work today.
The union, however, claims there will be significant delays to customers.
First Union organiser Tali Williams said the impact could be worse in places with fewer banks - such as small towns - where there would be fewer staff to carry the workload.
"The impact is in [the] number of staff who are available to carry this work out.
"So say for example in a city where there's lots of different branches, the impact may be [not as bad as], say, in a town where there's one branch and those guys are going out."
Ms Williams said Christmas Eve was traditionally a busy day for banking and customers.
"As they rush around to get their last-minute shopping done, perhaps go into a bank branch to get money out - so those people may be impacted, and same with those who want to do a bit of online banking."