A Brisbane mother has been jailed for 18 months after she abducted her two children and went on the run for three years.

Supporters of the 49-year-old mother wept as she was taken into custody, with Federal Circuit Court Justice Michael Jarrett ruling she had shown "flagrant disregard" for a custody arrangement with her ex-husband.

The children's 74-year-old grandmother, who has cancer, was also jailed for a minimum of three months because she kept the location of her daughter and grandchildren secret.

The children's mother, who cannot be named for legal reasons, had claimed her ex-husband was violent, abusing the children and threatening her life.

But Justice Jarrett said he was "completely unsatisfied" that the mother had proven the allegations.

In 2014, after the Family Court ordered an even custody split between mother and father, the mother used a secret network of helpers to escape Brisbane with the children and hide from authorities.

It is understood that with the help of the network they moved to several locations and were able to stay off the grid, staying clear of using phones and bank accounts.

However, the Australian Federal Police located the mother and children north of Brisbane late last year, after they moved into the grandmother's home.

The children were returned to the father and continue to live with him.

The woman's children were deprived of any chance to build a relationship with their father, Justice Jarrett said. ( Supplied )

Children subjected to 'trauma'

It is understood the mother was never charged with abduction or other criminal offences.

But on Friday she pleaded guilty to contempt of court for breaching the custody arrangement.

Justice Jarrett said the mother's offending was "significant".

"[The mother's] non-compliance with the orders have deprived these children the opportunity of developing their relationship with their other parent," he said.

"Even more significant is trauma these children have been subjected to as a result of many shifts from residence to residence."

Justice Jarrett said the mother had shown no remorse for her actions, and a fine was inappropriate given the "gravity of contempt".

He jailed her for 18 months and ordered her to serve the full sentence.

The children's grandmother also pleaded guilty to contempt of court and was handed a six-month custodial sentence, suspended after three months.

The court heard the grandmother had been ordered to provide any information about the whereabouts of her daughter and the grandchildren, but harboured them for nearly six months without informing authorities.

Outside court, a lawyer for the women said they would not appeal the sentence.