An integral discrete ordinates method designed for use on modern, large-memory, vector and/or parallel processing supercomputers has been developed. The method is similar to conventional Sn techniques in that the medium is divided into spatial mesh cells and discrete directions are used. However, in place of an approximate differencing scheme, a nearly exact matrix representation of the streaming operator is determined. Although extremely large, this matrix can be stored on today’s large-memory computers for repeated use in the source iteration. Since the source iteration is cast in matrix form, it benefits enormously from vector and/or parallel processing, if available. Several electron transport test results are presented demonstrating a reduction in numerical diffusion and elimination of observable ray effects.