The workers belong to the Broadcasting, Entertainment, Cinematograph, and Theatre Union, known as Bectu. In a ballot held by mail over the last two week, 94 percent voted for a strike.
The major issue in the labor dispute is pay. The union has reportedly asked for a 5 percent pay raise; management has offered 2.77 percent.
According to the BBC, the union has not set a date for a strike.
The vote is the latest blow in a difficult month for the company. In late November, artistic director and CEO Sešn Doran stepped down; three weeks later, chairman Martin Smith departed, in part because of outrage at the speed and lack of transparency with which the company replaced Doran.
The strike vote was prompted in part by the chaos at the top of the organizaton, Gerry Morrissey, a Bectu official, told the BBC. "The ballot result indicates the level of dissatisfaction the staff have with the board," he said. "Instead of uniting the organization after the recent departure of the chairman and chief executive they have chosen confrontation with the union over pay."