A monoenergetic neutron beam simulation study was carried out to determine the optimal neutron energy range for treatment of rheumatoid arthritis using radiation synovectomy. The goal of the treatment is the ablation of diseased synovial membranes in joints such as knees and fingers. This study focuses on human knee joints. Two figures of merit are used to measure the neutron beam quality, the ratio of the synovium-absorbed dose to the skin-absorbed dose, and the ratio of the synovium-absorbed dose to the bone-absorbed dose. It was found that (a) thermal neutron beams are optimal for treatment and that (b) similar absorbed dose rates and therapeutic ratios are obtained with monodirectional and isotropic neutron beams. Computation of the dose distribution in a human knee requires the simulation of particle transport from the neutron source to the knee phantom through the moderator. A method was developed to predict the dose distribution in a knee phantom from any neutron and photon beam spectra incident on the knee. This method was revealed to be reasonably accurate and enabled one to reduce the particle transport simulation time by a factor of 10 by modeling the moderator only.