Several one-energy group, discrete-direction radiation transport systems having analytic flux solutions are presented as an aid in Monte Carlo benchmark analysis techniques independent of realistic geometry and cross-section data requirements. Exact comparison of analytic and Monte Carlo results to several significant digits is possible for up to 26 directions in one, two, and three dimensions. A continuous direction model has also been formulated from an infinite limit of the discrete-direction model. Complete analytic flux solutions are possible through the imposition of boundary sources dictated by assumed exponential solutions of the transport equation. Extensions to two energy groups, two cross-section media, secondary particle production, time dependence, and continuous slowing down are examined. A website is provided from which codes and sample output files for the analytic and Monte Carlo models can be downloaded.