Duncan MacDougall and Przemek Krawczyk, who were named locally, were on board the Nancy Glen when it got in to trouble in Loch Fyne.
The alarm was raised by a third man who was pulled from the water by the crew of a passing boat at around 6pm on Thursday.
He told rescuers his vessel had capsized and there were two more fishermen in the water, off the Argyll and Bute coast.
Despite efforts of those on scene to keep it afloat, the 40ft fishing vessel has sunk.
A major search rescue was launched but more than 20 hours later the men had still not been found and the operation has been scaled back.
It is understood all of the Tarbert fishing fleet have also gone out to help with the search efforts.
A spokesman for Tarbert and North Kintyre Churches said: "This is a close-knit fishing community and everyone is absolutely devastated by what has happened.
"The Church of Scotland and Free Church of Scotland are working closely with Matthew Ramsay of the Fishermen's Mission in Argyll to support the community and the emergency services personnel involved in the search operation.
"Our thoughts and prayers go out to everyone affected by this heart breaking incident."
Julie-Anne Wood, head of maritime operations for HM Coastguard, said: "We are in regular contact with the missing men's families.
"It is a very distressing time for them and the local community as a whole.
"The search will continue until dark tonight and will resume again at first light tomorrow."
The casualty who was recovered from the water was transferred to Mid Argyll Community Hospital in Lochgilphead, where staff describe his condition as stable.
Police and the Marine Accident Investigation Branch (MAIB) are carrying out a joint investigation to establish what caused the incident.
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