The council gave notice last month that it intended to cut up to 500 jobs in response to a£12 million budget shortfall.
No sector had been singled out for the cuts, with every department reviewing its budget, it said.
But Unison is angry that staff found out about the cuts from the media rather than from management. It says there was no consultation or consideration of other savings.
Branch secretary Sue Donnelley said that when the union was first told of the job losses, letters from the council to staff had already been prepared for distribution.
'Members want to send a message loud and clear about the depth of anger over the insensitive way this has been handled,' she said.
A council spokeswoman said it had to release the information in December to give the three months' notice required by law. Employees had a right to know as soon as the decision was made.