First Union said union members at ANZ were voting on a national strike ballot and local strike action had already begun.
The ballot followed a second round of employment negotiations after 98.5 per cent of the bank's union members rejected a previous proposal from ANZ.
"Insecure work may suit the boss but it is unfair and does not work for workers," said Gay. "And for New Zealand's wealthiest bank to try and impose more insecurity is disgraceful."
An ANZ spokesman said less than 20 per cent of the bank's staff were union members.
First Union and ANZ had entered into collective employment agreement negotiations, as the current two-year agreement had expired, the spokesman said.
"None of ANZ's proposals reduce the job security of staff," he said. "The flexible working proposal simply allows us to make changes to the days and start/finish times of some new employees from time to time to ensure we can match staffing levels to the demands of our customers and respond to any changes."
The spokesman said ANZ paid its staff very competitively compared to similar jobs in the market and the salary ranges for almost all jobs covered by the collective agreement were the highest in the banking sector.
ANZ had offered staff pay increases of between 2.75 per cent and 3 per cent over the next two years, which was well above inflation and the average increase in New Zealand wages, the spokesman said.
"It is disappointing that the union are encouraging staff to take strike action when there is such a good offer on the table."
The spokesman said only one branch had taken strike action, for one hour, so far.
Gay said the bank's proposals would result in the most significant changes to terms and conditions of employment agreements since the amalgamation of the ANZ and National Bank under the single ANZ brand.