The neutron transport equation in toroidal geometry is numerically solved by making use of the discrete-ordinates SN method. The computer program developed for this computation is capable of treating a multigroup problem with anisotropic scattering. Numerical examples are given for the first wall and blanket system of a conceptual tokamak reactor design that has an aspect ratio of ∼3. To validate the present method, several numerical comparisons have been made with Monte Carlo results as well as with ANISN calculations in the case of an infinite major radius. The toroidal geometry calculation, with a uniform neutron source distribution throughout the plasma region, yields a neutron flux that, at the first wall, is maximum near the top and bottom of the torus. As one moves radially outward from the first wall, the position of the maximum flux rapidly shifts to the outermost point of each poloidal circle, and the flux decreases monotonically along the poloidal circumference until it reaches a minimum at the innermost point of the torus. At ∼10 cm from the first wall, for example, the variation becomes >20%. The one-dimensional infinite cylinder calculation shows an overestimate of flux within the first 1 cm of the first wall compared to the present calculation. In the rest of the first wall and blanket system, the one-dimensional model underestimates the fluxes in the outer region of the torus and overestimates the fluxes in the inner region.