Claire Pinkney, 35, from Swalwell in Gateshead, was last seen at her home address on Tuesday evening, November 29.
Officers believe that Claire and her two sons (aged 8 and 3) have travelled, by National Express coach, from Newcastle to Liverpool on Wednesday morning.
They may now be in the Liverpool or Cheshire areas and Northumbria Police are working with officers in those areas to try and locate them.
Claire is 5ft 4ins tall, of slim build and has dark hair, possibly tied up. She was last seen wearing a black poncho.
The 8-year-old is around 4ft tall, has short dark hair and was wearing a grey padded jacket. The 4-year-old has short blonde hair and was wearing a navy blue hooded top.
Anyone with any information as to Claire and her children’s whereabouts is asked to contact Northumbria, GMP or Merseyside police on 101.