Twenty-six small white coffins were lined up under a marquee as local community and political leaders said goodbye to the children.
The children and their teacher were killed when their primary school collapsed. Two other women lost their lives during the earthquake in the southern Italian town.
Applause punctuated by wailing greeted the coffins - bedecked in white flowers, some with a toy or a message - as they were carried from a sports hall turned mortuary to a large tent.
The funeral service was held there as the village's church was also damaged in the tremor and then the coffins were taken up a hill to the cemetery for burial.
Correspondents say the grief of the children's parents was being shared across Italy, with almost every family expected to watch the funeral on live television.
Questions remain about why the relatively modern school was the worst hit building in the mediaeval town, and why the children were still there when earlier tremors had led to school closures elsewhere.
San Giuliano has now been evacuated completely, with residents sent to friends or family elsewhere or living in tents erected in a valley below the village.
But the mass funeral has brought everyone back to the devastated area, along with Italian President Carlo Azeglio Ciampi, who earlier visited a hospital where some of the children pulled alive from the rubble of their school are being treated.
Monsignor Tommaso Valentinetti, one of six bishops to hold the funeral ceremony with the village's priest, addressed the president when he pleaded for San Giuliano not to be forgotten once the dead were buried.
"I want to say one last thing to those who are representing the state, public life: help us more than ever to keep a watchful eye for those tragedies not to happen, to prevent them, for such a terrible experience never to be repeated.
"Help us in keeping a watchful eye, help us in prevention."
Mother's wish
His plea was echoed by one of the grieving parents, Nunziatina Porrazzo who told the service: "On behalf of all mums and dads, we give to the Lord these angels of ours, the angels of San Giuliano.
"They are close to us, we are lucky because we have their faces close to us," she said through tears.
"I ask only one thing from all of you: for our schools to be safer.
"I absolutely want no mum or dad to mourn their children any more."
The Christian names of all the victims - including an entire class of six-year-olds - were read by Monsignor Valentinetti at the makeshift altar as the congregation listened in sad silence.
The service was held outside to avoid any risk of mourners being hurt by loose debris from the village's buildings, which have been heavily damaged, as aftershocks continue to shake the region.
Investigations
State prosecutors have begun investigating whether manslaughter or criminal negligence charges should be brought over the collapse of the school.
There is rising anger among local people following the discovery that local bureaucrats had failed to take any action despite the area being designated a medium-risk earthquake zone as recently as four years ago.
However, prosecutor Maria Teresa Perna said no individual was yet under investigation for the collapse of the 50-year-old school, which had only recently been modernised.
The Italian Government is to hold an emergency cabinet meeting later on Sunday to vote for new funds for earthquake relief.
A total of 8,000 people have now been evacuated from towns across southern Italy, with families taken to makeshift tent cities set up by civil authorities.