We present a highly parallel graph mapping technique that enables one to efficiently solve unstructured grid problems on massively parallel computers. Many implicit and explicit methods for solving discretized partial differential equations require each point in the discretization to exchange data with its neighboring points every time step or iteration. The time spent communicating can limit the high performance promised by massively parallel computing. To eliminate this bottleneck we map the graph of the irregular problem to the graph representing the interconnection topology of the computer such that the sum of the distances that the messages travel is minimized. We show that, in comparison to a naive assignment of processors, our heuristic mapping algorithm significantly reduces the communication time on the Connection Machine CM-2. *Visiting Research Associate, Research Institute for Advanced Computer Science, NASA Ames Research Center, Motfett Field, CA 94035 and Ph.D. Student at 11ensselaer Polytechnic Institute, Troy, NY 12180. ISenior Scientist, Research Institute for Advanced Computer Science, NASA Ames Research Center, Moffett Field, CA 94035.