A method and an apparatus for predicting interference, at practical accuracy and calculation time, between a target section of a robot and a peripheral object installed around the robot, when the target section, such as a tool or a sensor attached to a robot hand, is moved along a movement path thereof due to the motion of the robot. A convex hull, defined by areas occupied by the tool at adjacent time points, is calculated. It is judged whether a common area exists between the convex hull and a polyhedron area. When the common area exists, it is judged that the tool interferes with the container box on the movement path, and the procedure is terminated. When the common area does not exist, it is judged whether j