McElkerney’s Requiem Mass took place at St Peter’s Cathedral in west Belfast at 11am, followed by cremation at Roselawn Crematorium.
A large crowd of men, many with their faces covered and wearing berets, led the funeral procession.
His coffin was draped in the tricolour and the starry plough flag.
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Father Gary Donegan told mourners that McElkerney’s death was a “tragedy”.
The 57-year-old was taken to hospital after he was discovered critically injured at Milltown Cemetery in Belfast last week.
He died later from his injuries.
He was thought to have been, at one time, the leader of the INLA in Belfast.
On Monday night, shots were fired during a paramilitary-style display outside his Belfast home.
Social media footage showed a masked man wearing a white shirt and black tie discharging several rounds skywards.
Another video shows around 20 masked men in a guard of honour as a coffin arrives.
McElkerney was jailed in 1987 for his part in a 1982 boobytrap bomb which killed two schoolboys, Kevin Valliday (11) and his friend Stephen Bennet (14), as well as 20-year-old Lance Bombardier Kevin Waller.
He was released in 1999 under the terms of the Good Friday Agreement.
At the funeral, Fr Donegan said McElkerney had joined the INLA following the death of his friends during the Troubles.
He added: “Those were sad and difficult times, and are hardly recognisable 21 years after the Good Friday Agreement which saw Martin released from Long Kesh after a decade and a half of incarceration.
“Following his release from prison, Martin became aware that the choices he made in life, had significant and lasting consequences for others, including his family.”
The priest added that McElkerney’s organs had been donated following his death.