A 32 node parallel processing computer will be used at the San Diego Supercomputer Center to investigate a variety of problems in theoretical elementary particle physics whose solution requires a high degree of computational power. The problems will be tackled by replacing the continuum of space and time by a discrete lattice of points. This approach will be used to calculate quantities relating to the masses of the elementary particles and to the behavior of these particles with respect to both the strong and the weak nuclear forces. It is hoped that progress will be made on major questions that cannot be addressed in any other way. Techniques for effectively carrying out physics computations on highly- parallel processors will be developed.