AUSTRALIAN mother Allyson McConnell drowned her two young sons in a bathtub before driving to a restaurant, ordering lunch and then jumping off an overpass onto a busy freeway, a Canadian court has heard.

Ms McConnell is charged with the 2010 second-degree murders of two-year-old Connor and 10-month-old Jayden in Millet, south of Edmonton.

The trial began in Wetaskiwin, Alberta, today.

Ms McConnell, 33, formerly of Gosford on the NSW central coast, moved to Canada in 2005, met local man Curtis McConnell and married him in 2007.

Prosecutors said the marriage deteriorated, Ms McConnell was angry with her estranged husband and wanted to take their sons back to Australia.

The court was told on the day before the boys were killed, Ms McConnell tried to give away the children's clothing and a car seat.

After Ms McConnell drowned the boys in the family bathtub she drove to a restaurant, ordered lunch and then left upset, it was alleged.

She walked to the overpass and jumped off, suffering numerous broken bones, the court heard.

The Crown alleged police searched her home and found a rope tied to the rafters in the basement.

The trial continues.