The Irish Postmasters' Union says the strike by postal machine maintenance workers should not be happening in the year 2015.
Staff members responsible for equipment in An Post's mail centres are striking over cuts in pay.
The 36 staff involved are members of the Communications Workers' Union and employees of I-O Systems.
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As a result, An Post's mail services has been suspended since yesterday.
General Secretary of the Postmasters' Union Ned O'Hara, says An Post needs to engage with I-O Syetems and the workers' union to protect the service: