They were among four people who were on Irish Coastguard Rescue 116 helicopter when it crashed on Tuesday.
The funeral for pilot Captain Dara Fitzpatrick was held on Saturday.
The search, which has been impeded by adverse weather, will also focus on finding the wreckage of the helicopter.
The priority for those involved in the multi-agency operation has been to recover the bodies of chief pilot Mark Duffy and winchmen Paul Ormsby and Ciarán Smith.
Heavy swells have so far prevented those involved from getting near to the site where a signal from the helicopter's black box was located close to Blackrock Lighthouse.
Search crews hope the missing crew will be located in the wreckage of the helicopter.
The Commissioners of Irish Lights ship Granuaile left Galway on Saturday evening after being loaded with specialist equipment, including a Remotely Operated Vehicle (ROV) that could be used to access difficult to reach undersea areas.
The vessel is equipped with a 20-tonne crane, which could be used to lift wreckage from the sea bed.
A surface water search resumed on Sunday morning involving coastguard units, the RNLI and Irish naval ship LÉ Eithne in addition to extensive coastline searches at Belmullet and Achill.
Naval divers are on standby and will be deployed as soon as conditions permit.
Captain Fitzpatrick was recovered from the sea, hours after the helicopter crashed in the early hours of Tuesday morning.
She was the mother of a young son and the most senior pilot with CHC which runs the contract to provide search and rescue services in the Republic of Ireland.
Hundreds of mourners attended her funeral at St Patrick's Church in Glencullen, County Dublin.
Members of the Irish coastguard formed a guard of honour and the coastguard helicopter did a fly-past.

Shortly after midday, the FTSE 100 was 37.55 points higher at 6,256.81.
M&S shares sank 8% after the retailer warned of a hit to short-term profits as it attempts to revive its clothing business.
New chief executive Steve Rowe says he intends to lower clothing prices and reduce the number of sales promotions.
But bank shares helped to bolster the wider market, with RBS up 3.6% and HSBC 3.4% higher.
Royal Mail shares rose 1% to 526.5p after regulator Ofcom said it would not impose any new price controls on the company.
Ofcom said it had decided against new controls because of the declining market for letters and increasing competition for parcel deliveries.
Electrical goods and mobile phone retailer Dixons Carphone rose 0.5% as it pushed up its full-year profit forecast after enjoying strong sales. It now expects profits of between Â£445m and Â£450m.
On the currency markets, the pound rose 0.3% against the dollar to $1.4685, and was also 0.3% higher against the euro at â‚¬1.3174.

The female was found in the Llandovery area last month, struggling with a fever and dehydration.
She was rehabilitated by RSPCA staff at a specialist wildlife facility in Taunton, Somerset.
Her weight also increased from 2.8kg to 4.8kg by the time she was released near to where she was found.
A ship with specialist equipment has arrived at Blacksod Bay off the County Mayo coast to assist in the search for three missing Irish coastguard members.
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(Noon): Banking shares helped to lift the market, but shares in M&S slid after the retailer said its turnaround plan was set to hit profits.
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An otter has been returned to the wild in Carmarthenshire after being found curled up in a puddle of water from a pressure hose.