The corpses were discovered in the family's home in Böheimkirchen in Lower Austria on Thursday.
Detectives say that Martina R. (35) shot her family whilst they slept. It's not clear why they didn't wake up when they heard the shots. Martina's mother (59) had recently been diagnosed with pancreatic cancer.
Police say it's possible that Martina R. killed her family on November 20th, and then shot herself some days later. Detectives believe that she had money worries, and was also involved in a dispute with the father of her children about his visitation rights.
The autopsy results are expected later this week.
Neighbours say that the family kept to themselves and were very quiet, and that even the children (a girl aged seven, and two boys aged nine and 10) didn't socialise with their friends at home.