A travel assist apparatus includes a calculator that calculates rear lane shape information in a section from a current position of the own vehicle to a rear position, on the basis of a lane information group and a traveling trajectory of the own vehicle. The lane information group includes pieces of lane information detected on the basis of images captured by an imaging unit successively during a data acquisition period. The pieces of lane information each includes information regarding relative positions of lanes with respect to an own vehicle. The data acquisition period is a predetermined period from a current time to a certain time in past. The traveling trajectory of the own vehicle is that during the data acquisition period and is calculated on the basis of a result of detection of both a vehicle speed and a yaw rate of the own vehicle during the data acquisition period.