More than a thousand Sellafield workers have voted for a strike action.
Unite the Union said 98% of workers, who are employed at the Sellafield nuclear site in Cumbria, backed the industrial action.
The decision follows a 10-month dispute over health and safety issues and being refused a full-time union representative.
They are currently looking to the management of Sellafield to reason with their requests and will decide what action to take at a meeting next Tuesday.
Unite regional officer Steve Benson said: “Our members have lost patience with Sellafield management who have steadfastly continued to ignore our very reasonable request.
“All they are asking for is their rights for a co-worker to become a union shop steward at the Sellafield site to represent construction workers and keep them safe. It makes sense for our members and the company and it will help improve industrial relations and a safety and welfare culture at the site.”
He added Unite members “have no wish to take action but are being forced to do so by a company unwilling to take our members’ concerns seriously”.
A Sellafield spoke person said: “Sellafield Ltd is not directly involved in the potential dispute, which does not involve any of our employees, but we will be monitoring the issue closely. We hope all parties can reach agreement as soon as possible. Safety and security at the site will be unaffected by any resulting industrial action.”