UPM’s mill at Rauma was closed last week and was joined by many of the company's other production facilities across Finland over the weekend.
Both UPM and Stora Enso face difficulties in storing paper reels weighing each around 1.5 tonnes.
The forest industry puts financial losses from the strike at 30 million euros of lost exports per day. Technological sector businesses, which account for 60 percent of Finnish exports, say their losses are twice as great.
Stainless steel manufacturer Outokumpu also faces difficulties as it is unable to export via the plant's nearby harbour in Tornio. The company fears a shutdown of operations by the end of the week if the strike continues.
National Conciliator Esa Lonka has called both sides in the dispute to fresh talks on Tuesday. The main bone of contention remains union demands on severance pay levels for stevedores made redundant. The Transport Workers' Union AKT is demanding one year's severance pay, a demand rejected by employers.
Stevedores commenced their strike action in the country's ports last Thursday morning.