Computer Sciences Corporation (CSC) which provides services to companies across Britain announced plans to axe 640 jobs on Monday.
The firm which has started a formal 90-day consultation with unions said: "This action is necessary because the IT services market is changing and our customers want competitive, new services with different contract and delivery models."
But the Unite union said the announcement was a "body blow" which had left employees "devastated."
Unite said the news meant that 1,100 job losses have been announced by CSC since February.
After several weeks of consultation over a reduction of staff working on an NHS contract, the move had come "totally out of the blue," according to Unite.
National officer Kevin O'Gallagher said: "This announcement of a further 640 job cuts has dealt our members a severe body blow and left them absolutely devastated.
"We have put forward a detailed plan which will avoid any compulsory redundancies in the company, however these plans have not been taken up and CSC is insistent on issuing compulsory redundancy notices despite receiving sufficient number of volunteer requests to leave the company.
"With the full support of our membership, Unite is determined to avoid any compulsory redundancies which are clearly unnecessary and in the main to enhance the profits of its American shareholders," said Mr Gallagher.
"We now owe it to our members to do everything in our power to support them during this very uncertain time and fight these job cuts."