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.
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.