Sian Duili, 47, and daughter Aisha were last seen in Barry, South Wales, on Tuesday but they are believed to have travelled to the north of England and Scotland.
South Wales Police said concerns are growing for their welfare and officers are appealing to the public to help track them down.
A police spokeswoman said: “It is believed that they have travelled to the Cumbria area, north of England, and then into Scotland.
“Sian has links to the Newcastle and Swindon areas.”
Anyone with any information on their whereabouts should contact 101, quoting reference 1800467620.