A mother has been charged with the murder of her two sons at their home in the NSW Blue Mountains.

Nine-year-old Ben and his brother Russell, 11, were found dead by their father when he arrived at their Chapman Parade home in Faulconbridge about 12.40pm on Tuesday.

The boys’ 42-year-old mother, Trish Smith, was also found at the home with stab wounds and taken to Westmead Hospital under police guard.

Ben and his older brother Russell, pictured fishing on the banks of a river.
Nine-year-old Ben and his brother Russell, 11, were found dead by their father on Tuesday. (Supplied: NSW Police)

Police said tonight that Smith had been released from hospital today and taken to Parramatta Police Station, where she was charged with two counts of murder (domestic violence).

She has been refused bail and will face court tomorrow.

Prime Minister Anthony Albanese and NSW Premier Chris Minns earlier this week addressed the incident, both saying it was a tragedy.

Trish Smith, 42, was taken to hospital under police guard.
Trish Smith was found with stab wounds and taken to Westmead Hospital under police guard. (Facebook)

Readers seeking support can contact Lifeline on 13 11 14 or beyond blue on 1300 22 4636.

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