Scientific and technological advances in the next 5 to 10 years will make it feasible to create an integrated, interactive system for the design, manipulation and analysis of collections of physical objects. These advances will come in computing power through the mechanism of parallel computation, in algorithms for geometry, in problem solving systems to provide very high level user interfaces and in graphics to allow direct visuali-zation of the behavior of the physical objects. In this paper we describe the project Com-puring about Physical Objects which is to explore the associated technical problems and to build prototypes of such systems. The focus here is upon the role of supercomputers in this area and, especially, their application to solving!.he partial differential equations that model many physical phenomena. I.