Myra Paea, 19, sentenced to two years' jail in the High Court at Gisborne on Thursday for manslaughter of her baby.

A teenage mother who shook her baby to death was an example of a young and inadequate parent who lacked the skills and maturity to raise children, a judge said as he sent her to jail.

Myra Paea, who was 18 at the time, was at her Gisborne home alone with her 7½-week-old son Milton Manihera Waikaaho Raroa when she became angry at his crying.

Milton died in Gisborne Hospital on December 2, 2014.

According to a summary of facts, Paea had been angry at him three times the previous day.

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The first occasion occurred when she wanted to go outside for a cigarette.

She picked Milton up and began forcefully rocking and shaking him. She did this for two minutes until he stopped crying.

She put Milton back in his pepi pod (a bassinet-like sleeping cradle), but he continued crying and she became more angry.

So she picked him up and shook him again, while yelling at him to "shut up" and "stop f...ing crying". When he stopped crying, she put him back in the pepi pod and went outside for a cigarette.

When she returned inside, Milton began crying again so she picked him up again and shook him until he stopped crying.

This time, he remained silent for three hours. When he woke up, Paea tried to give him milk, but he was not swallowing and was pushing it out. So she put him beside her on a mattress while she watched television.

At 6am the next morning, her partner woke up to find Milton gurgling. He picked him up, realised he wasn't breathing, and began CPR. When Milton failed to start breathing, he put him in his car seat, ran next door and asked neighbours to take them to hospital.

He then woke Paea and they all went to hospital.

Milton died at 10.38am. Hospital staff noted bruising to his face. He had head injuries, and an autopsy found these had caused his death.

Paea told police she had become "stressed out and frustrated" at Milton's crying, and had not been able to control herself.

Paea, now 19, pleaded guilty to manslaughter in the High Court at Gisborne on Thursday, and was jailed for two years.

Justice Geoffrey Venning said the circumstances of the case were "truly tragic", and any sentence must reflect what was a very serious crime.

"Children are defenceless and properly have to look to their parents and caregivers for safety.

"The consequences of shaking and striking babies is well known ... Regrettably, in New Zealand, such offending and the tragic outcome of it is all too common.

"Young and defenceless infants or children are killed by young and inadequate parents who do not have sufficient skills or maturity to enable them to cope with the responsibilities and demands of parenthood."

This was despite there being resources and support available in such cases, the judge said.

He noted that Paea had a personality disorder triggered by severe abuse when she was a child.

He also noted her early guilty plea, her immaturity, her sorrow and regret for Milton's death, and the fact that it appeared to be a one-off incident.

He said a sentence of home detention would not reflect society's concern for such offending, or act as a sufficient deterrent.