An evacuation travel assist apparatus includes a stop lane determination section that determines a stop lane and an evacuation place in the stop lane in which an own vehicle should be urgently stopped when the vehicle drive is detected to be in a state of being not able to drive the own vehicle properly, and a transverse position determination section that determines, as a stop transverse position, a position in a transverse direction of the evacuation place in the stop lane so as to ensure a space for the vehicle driver and passengers to get in and out of the own vehicle safely at a side of the own vehicle.