The Technical Engineering and Electrical Union (TEEU) is seeking an all-out picket from the Irish Congress of Trade Unions over its dispute in Dublin Port.
The dispute centres around a decision by the company to suspend nine fitters and electricians.
Over 30 members of the TEEU have been picketing Dublin Port from 7am after talks between unions and management at the company broke down last night.
Siptu workers in the maintenance section of the port have voted by 23 to one to support their fellow workers in the TEEU. The harbour section of Siptu, which represents pilots and radio operators, also voted by 23 to one to support the TEEU.
Clerical staff are voting after a meeting addressed by TEEU Regional Secretary Arthur Hall.
The union claims the company suspended its shore-based members for refusing work on board tug boats and to fill in for ship's crew when they are short-staffed.
But the company said the suspension resulted from the men's refusal to comply with a "reasonable management request" to undergo additional training. It said the request was in line with its agreements with the union.