Among the large problems for which teraflop (in principle massively parallel) machines will provide the means of solution are those involving the prediction of gravitational wave amplitudes from interacting strong field gravitational situations. Examples are neutron star/neutron star, neutron star/black hole, and black hole/black hole interactions, collisions, and mergers.While the weak field, long distance behavior of the gravitational field can be well treated by approximate methods, the strong field interaction and radiation regimes is full 3‐dimensional numerical analysis, apparently on grids of order (1000)3. Variable count amounts typically to about 80 variables per zone. Based on smaller scale evolutions running at about 0.2 to 0.3 Gflop/sec (Cray Y‐MP) which require ∼2×10−5seconds per zone cycle, one deduces ∼2×104seconds per cycle ∼6 hours/cycle for (1000)3(7×1011Bytes of memory required) runs. Because a typical run would require ∼104cycles, CPU times in decades would be required at Y‐MP CPU rates. Howevere, teraflop sustained machines would reduce this to the 6–10 hour range, and algorithm improvements would be expected to lower this by another factor of 10 (at least). Since there are a number of feasible designs for teraflow/sec machines, it appears the 2‐black hole problem will be double within the next five years or so. This paper discusses an outline for designing the code, discusses various alternatives in approach, and drafts a possible path through the forest of alternatives.