In an evacuation travelling assistance apparatus, a risk determining unit determines, when a driver is not in a state capable of appropriately performing driving operations, a risk involved in stopping at a location and a risk involved in passing through the location, for each of a plurality of locations that may serve as an advancing destination of the own vehicle, based on map information, own vehicle information, and peripheral environment information. An evacuation destination setting unit sets a location at which the risk involved in stopping at the location is lower than a predetermined reference as an evacuation destination, based on the determined risk. An evacuation route setting unit combines locations at which the risk involved in passing through the location is lower than a predetermined reference, based on the determined risk, and sets an evacuation route from the current position of the own vehicle to the evacuation destination.