[en] The F/sub N/ method is used in this paper in regard to two-group neutron-transport theory, to compute accurate critical dimensions for slabs and spheres. The F/sub N/ method has enjoyed considerable success in producing accurate numerical results for multigroup problems relevant to radiation shielding calculations. In these previous works, only downscattering was allowed, however, so now we consider a fully coupled two-group model to demonstrate the viability of the F/sub N/ method for a new class of problems