If that's what they say they want then let's see an offer that reflects that."
Predictable hours meant a secure family life, Ms Gay said.
The strike would lead workers into Labour weekend, and more industrial action was being planned for the next week. The union had also filed cases against the bank for discriminating against workers that had taken strike action.
A statement released earlier by the bank said the proposal of flexible rosters would not casualise jobs or reduce job security.
The average salary of employees on the collective agreement was $59,000, the statement said.
"ANZ has offered staff pay increases of 3 per cent and 2.75 per cent over the next two years.
"In addition, ANZ pays for medical/health insurance for all staff and provides all staff with discounted lending rates."
ANZ said its leave entitlements and other terms of employment were among the best in the industry.
"The proposal for flexible rosters does not casualise jobs or reduce the job security of staff," an ANZ spokesman said.
"Our customers want us to have some branches open later on some evenings or on Saturdays and Sundays, so we need staff to work at those times."