The ashes of stillborn babies and babies who died within days of being born were buried in cardboard boxes at Edinburgh's council-run Mortonhall Crematorium.
Since the crematorium opened in 1967 grieving parents were told by bosses there would be nothing to scatter after the cremation of their children.
But now it has been revealed the ashes of babies who were stillborn or who had died within days of being born were kept by the crematorium, and later buried in cardboard boxes.
It is feared the number of babies involved could run to hundreds.
Some parents were apparently lied to when they asked for their child's remains and were told there were none to collect.
The remains of many children were buried in a field behind the crematorium.
However, it is not clear whether the remains of all the children affected were buried there or, if not, what happened to the others.
The practice is understood to have been accepted policy at the crematorium for 45 years until last year when it was changed after the arrival of a new manager. It is not known whether the policy was devised by one official acting alone or approved by more senior managers at the local authority.
Helen Henderson, 43, from Sighthill, Edinburgh, said she has never recovered from the shock of being told she could not have her son's ashes, only to now find out they have been dumped in a box on crematorium land.
She said: "My son Nathan died when he was just one day old in August 2004.
"We were told by the undertaker we would receive his ashes, but when we went to collect them a lady at the crematorium told us we had been misinformed and that there was nothing for us to collect."
The city council has launched a probe into why the practice was allowed to develop at Mortonhall and environmental services convener, Councillor Lesley Hinds, has offered a full apology.
Sands Lothian, a charity that counsels parents who have lost a child through a stillbirth or neonatal death, uncovered the scandal.
The charity's operations manager, Dorothy Maitland, found out the ashes of her daughter Kaelen have been interred in the ground at Mortonhall, 26 years after she was told there would be nothing to collect.
She said: "It's come as a complete shock to me. For years I have had nowhere to go to put flowers, or grieve for Kaelen.
"The new manager at the crematorium has told me the only reason he can think why this happened in the past was either laziness or a bad attitude.
"We need to know how many babies' ashes are buried there."
Ms Hinds said: "I want to offer my deepest apologies to all those families who have been affected by this dreadful and completely unacceptable situation."