The body of Alexander Haywood (72), of Pleasant Point, was recovered from the lake early yesterday after Wednesday's mishap.
Mr Haywood's son, Antony (46), and Murray Green (54), both of Timaru, have not been found.
A spokesman for the Haywood family, Craig Coutts, of Timaru, last night declined to comment, other than to say "our prayers are out there for Tony and Murray".
Hope was fading last night of finding the two men alive, despite extensive land and lake searches.
Senior Constable Russell Halkett, of Fairlie, said it was unlikely the pair had survived.
"Anything is possible, but the ground and helicopter searches showed no evidence they had made it out," he said.
The search was suspended about 5.10pm, but options would be re-evaluated today.
Senior Constable Brent Swanson, of Tekapo, said: "Unfortunately, Lake Tekapo tends to swallow bodies and not give them back to us."
Search operations manager Ray Bellringer said the missing men might have made it ashore and crawled somewhere for shelter, then lost consciousness and been unable to hear searchers.
"There is still some hope we may find them alive."
Because Lake Tekapo was so cold - estimates range between 8degC and 10degC at this time of year - anyone in the water would not survive long, perhaps "one or two hours".
The trio left Pleasant Point about 6am on Wednesday and launched their 4m 1973 Flylight Fisherman boat, with its Johnson 90hp motor and an auxiliary, about 11am.
They headed for the top of the lake for a day's fishing, in choppy conditions with northwest to northerly winds gusting up to 30kmh.
When they did not return, a family member went searching.
Mr Bellringer suspected something happened "earlier rather than later" in the trip, because full Thermos flasks and bread rolls were found in the boat.
The throttle on the boat was fully open, which also indicated that whatever happened did so quickly.
It was suspected the mishap happened off the Cass River mouth.
Staff on a neighbouring station reported seeing a boat heading up the lake about 12.30pm on Wednesday.
An Air Force Iroquois with crew wearing night-vision equipment searched for the boat on Wednesday night, finding it shortly after midnight, but there was no sign of the men.
The swamped boat was on a sand bar 50m from the mouth of the Cass River.
The Westpac Rescue Helicopter from Christchurch started searching at first light yesterday.
Alexander Haywood's body was found in the water about 7am.
He was not wearing a life jacket, although they were on board, along with flares and a torch.
A large amount of flotsam from the boat was found.
Mr Bellringer said two boats were used to search the lake.
Ground search teams scoured the shoreline around the top of the lake and Motuariki Island.
Between 35 and 40 people, including maritime search and rescue personnel from Timaru and Department of Conservation rescuers from Mt Cook, were involved.
Snr Const Swanson said the boat was refloated and towed to Tekapo township where it was being examined last night by Maritime Safety Authority inspectors.
- Additional reporting The Courier, Timaru
