When performing a computer simulation on analytical study of robot motions it is possible to unwittingly require a part of the robot (e.g. the hand) to interpenetrate (i.e. to interfere with) another part (e.g. an arm). It is therefore important to be able to predict in advance whether self interference or collision of any type occurs. This problem arises in fields of interest other than robotics, e.g. computer aided design and computer graphics. In this report, we have developed a computational method which predicts interference of moving objects in space. The method works for non-convex solids and multiply-connected solids (solids containing holes). The method checks the boundaries of surfaces enveloping solids for interference. Every pair of surfaces (one on each body) are examined for points of intersection. Points of interest are then studied to determine whether any two solids do interfere. The theory is developed for planar, ruled, and double curved surfaces.