A Sydney woman who gave her two children rat poison before smothering them to death has been jailed for at least four years.

In sentencing the 31-year-old woman, NSW Supreme Court Justice Clifford Hoeben on Friday accepted she had shown remorse for the two killings.

She pleaded not guilty to murder on the grounds of mental illness, but was found guilty of the manslaughter of her four-year-old son and two-year-old daughter.

Justice Hoeben concluded the Canley Vale woman, who cannot be named for legal reasons, had been suffering "substantial impairment by abnormality of the mind" at the time of the killings.

The court was told the severely depressed woman fed her children rat poison mixed with sugar and water in February, 2008.

Fearing the poison wouldn't work, she used a pillow to smother her daughter and her hand to suffocate her son.

The judge said she had been angered by her husband's infidelity.

The woman sobbed quietly in the court as her sentence was handed down.

With time already served, she will be eligible for parole in February, 2012.

Justice Hoeben said the woman posed no threat to the community and set a maximum term of six years.

The father of the children, who found them dead on the day of the crime, was not present in court on Friday.