The pair became lost off the Mataikona rocks as part of a group of four close family members based locally in the Wairarapa.
"It appears they were looking to get pāua from the reef systems there, perhaps not looking to go out too deep, just in a channel," Matheson said.
"Three of them went into the water. One decided the conditions weren't particularly good and told the others that he was going back in.
"Unfortunately by the time he got back in the other two had disappeared. The sea conditions weren't good around the rocks."
The search for the pair was undertaken quickly by rescue helicopters, with the aid of around 10 nearby fishing boats at Castlepoint.
"It was a very close family group. It's just soul destroying really for those involved."
The Police National Dive Squad was also out this morning.
A further low-tide search by Amalgamated Helicopters was expected to take place around 1pm.
Wairarapa Search and Rescue sergeant Tony Matheson expressed the police search operation's fears for the pair's safety, but said they have "excellent search conditions today".
"We have grave concerns for the pair's safety and we are working as hard as we can to find them," Matheson said.
It is understood the family were fishing without fins but Matheson said that was not unusual.
"Some of the reef systems in the Wairarapa, you've only really got to have a wetsuit and some booties, a mask and snorkel to wander round some of the rock pool areas to gather sea food," Matheson said.
"Mataikona coast line is quite a rugged reef system. It's sort of protected by the weather a lot of the time. But the conditions can be quite rough.
"Obviously something quite bad has happened out there for them not have made it back to shore."
Riversdale Surf Life Saving Club chairman Dave Rose said they would be supporting the police dive squad at midday at Mataikona.
"We'll be taking members of the police dive squad out to recommence the search. We were involved yesterday for about five hours just looking close to the coastline," Rose said.
"At the moment we're still holding out hope that the two of them managed to get to shore somewhere.
"It is quite a tough coastline with rocky areas."
Rose said some people lived, and others holidayed, on the coastline where the father and son went missing.
"It's a good little community and they'll be shattered by this. There's a number of people that holiday there," Rose said.
"It's not a big community but they're quite close knit and this will obviously be a tragedy for them up there."
Yesterday, an initial search included the Westpac Rescue Helicopter and Amalgamated Helicopters, the Lady Elizabeth IV launch, three commercial fishing boats, the Riversdale Surf Life Saving Club, and a large number of private fishing vessels that had been part of a fishing competition.
