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. The risk determining unit evaluates, for each of the plurality of locations, at least one evaluation subject among a plurality of evaluation subject including: a risk occurrence frequency at the location; a risk avoidability at the location; and a level of danger of the risk occurring at the location, based on a plurality of levels, and determines the risk involved in stopping at each location and the risk involved in passing through each location, based on evaluation results.