The employees will participate in the ballot after a previous 1.5% pay rise offer from Sellafield Ltd was rejected.
Union GMB said with the RPI inflation rate currently 3.5%, last year Sellafield workers received just 0.25% extra pay against annual RPI inflation for 2016 of 1.8%.
And with new government led changes to the pensions of nuclear workers coming into effect from next year, the union said two thirds of Sellafield workers will also have to pay an extra 2% to 6% on their pensions.
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Chris Jukes, GMB Senior Organiser, said: "GMB members at Sellafield Ltd understandably voted by 9 to 1 to reject the company's pay offer which was less than half the RPI inflation rate.
"GMB's repeated requests for further talks have been ignored and the company has instead said it will impose its below inflation pay rise.
"With Sellafield refusing to meet us, GMB has little alternative than to ask our members if they wish to take strike action to achieve a fair pay offer."
Unite regional officer, Graham Williams, also added that the pay increase was "completely unacceptable".
"There has been a sustained erosion of pay, and terms and conditions in recent years including a proposed new pensions’ package with reduced benefits and new starters employed on inferior conditions," he said.
"The current regrading exercise would reduce craft pay by a minimum of £5,000 a year. The management now needs to come to the table and negotiate in a constructive manner, otherwise possible future industrial action could bring Sellafield to a halt."
The strike ballot will begin on Monday, 14 August. It will close on Monday, 04 September.
(LM)
