This project will study the feasibility of a petaflops-class computer for use in particle simulations in astrophysics and other areas of computational science. The planned system will operate by performing the most CPU-intensive part of a simulation (the computations of long-range interparticle forces) in hardware, leaving the remainder of the calculation to a front-end host computer of more traditional design. Confidence in the basic structure of the hardware is strengthened by the success of the 1.1 Tflops "GRAPE-4" system, which has a similar design philosophy and became operational on 1995. Utilizing straightforward improvements in fabrication technology, a petaflops machine is a realistic goal by the year 2000. Significant questions must be studied to refine design ideas, explore configuration option, and ensure the widest applicability of the new machine. A number of target problem areas in astrophysics, with a wide range of spatial and temporal scales, have been identified. Preliminary estimate suggest that substantial gains will be realized over the conventional general-purpose supercomputers likely to be available in the year 2000, with a time advantage of over a decade in some cases. Outside astrophysics, the subject most likely to benefit from a special-purpose computational engine of this sort are molecular dynamics and vortex fluid methods.