Greyhound Recycling is to apply for a High Court injunction to prevent what it calls unlawful picketing at the Clondalkin facility.
Workers have been on strike for eight and a half weeks in a row over proposed pay cuts of 35%.
The company says the protest at the gates of the plant is preventing the collection of waste in some areas, which in turn is posing a health and safety risk for residents whose bins are not being emptied.
SIPTU's Stephen Lewis appealed to Greyhound's senior management to allow the staff to return to work while they negotiate an agreement.
"As has been our position from the outset, we're calling on (CEO) Michael Buckley to allow these men to return to work until we reach an agreed settlement that satisfies both the company and SIPTU," he said.