Critchley Labels, based in Crumlin, also faces disruption of its business outlets as far afield as Australia, Japan and the United States.
The company, which makes specialist labels for electronics products, has been picketed since the workers were sacked two years ago in a long-running dispute over union recognition.
Communication Workers' Union national officer Simon Sapper said the "techno-strike" was the largest-scale action of its kind ever mounted in Britain.
"Critchley are still in the Stone Age in terms of industrial relations. All we are seeking to do is to persuade them to take a responsible attitude and sit down and negotiate a settlement of this dispute," he said.
"Our members, and those who support us, can make an effective protest from anywhere in the world having to go anywhere near the factory."
A more traditional event is being mounted by the union next week with a march and rally to mark the anniversary of the dispute.
A Critchley spokesman said it was "a sad misdirection of action against a profitable company".
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