The paper workers' union says UPM workers could go on strike from 2 January if a deal isn't reached with the company over a new collective agreement.
Union bosses announced the strike threat on Tuesday after a meeting during which they approved deals with seven other firms, including the giant Metsä Group.
Those deals reflect current conditions in the sector and the pay rises already agreed elsewhere in this round of pay talks.
UPM plants would be closed for three weeks during the strike, unless a deal is reached.
The union says that it is unable to agree to five separate agreements depending on the business sector, as UPM is demanding.
The collective agreement currently governing pay and conditions in the paper industry is the fiftieth and last sector-wide agreement, after the employers' side announced they preferred to negotiate company by company.
In Finland industrial action is permitted when no collective agreement is in force, but are deemed illegal if they take place after a deal has been agreed.