They're looking for Liza Parker, 26, Mason Worcester, 5, and Tiaona Robinson, 1.
Police said Parker and the children were expected to arrive at a scheduled appointment Sunday night, but they never arrived.
They said that's out of character and the criminal investigation division has launched an investigation.
Parker and her children were last seen Sunday afternoon in Bangor.
It's possible they could be in the Ellsworth area.
Parker drives a silver 2007 Mazda, CX-7 with Maine license plate number 9018 WD,
Bangor police hope to hear from anyone who has seen Parker and her children.