The 265-foot Swanland with a crew of eight was carrying 3,000 tons of limestone and went down in gale conditions early Sunday about 30 miles northwest of Wales' Lleyn peninsula, the BBC reported.
Three crew members were rescued soon after the sinking, although five men were still missing, the British military said. One of the men found clinging to debris died, The Guardian said.
The Royal Air Force said it had four helicopters taking part in the search for the missing men and numerous commercial ships also converged in the Irish Sea.
An empty lifeboat from the Swanland was found on a small island off the coast, the BBC said.
Coast guard spokesman Jim Green told the broadcaster the missing men were in cold and turbulent waters, but there was still hope.
"We know that at least some of them are wearing immersion suits and have strobe lighting with them, however sea conditions are challenging at best," Green said.