Kristina Pikse, 28, and her three children were last seen in Glasgow's Pollok area a week ago.
Ms Pikse may have travelled to Blackburn, Lancashire, with eight-year-old David Hauberts, his brother Danius, four, and sister Zana, aged nine months.
She is described as very slim with long, dark hair, brown eyes and sallow skin.
A Police Scotland statement said: "It is believed that the family may have travelled to the Blackburn area, however despite extensive enquiries officers have been unable to trace Ms Pikse and her young family.
"Anyone who has seen them since Tuesday August 26 or knows of their present whereabouts is asked to contact Pollok police office on 101."