A potential application of the 10B(n, alpha)7Li nuclear reaction for the treatment of rheumatoid arthritis, termed Boron Neutron Capture Synovectomy (BNCS), is under investigation. In an arthritic joint, the synovial lining becomes inflamed and is a source of great pain and discomfort for the afflicted patient. The goal of BNCS is to ablate the synovium, thereby eliminating the symptoms of the arthritis. A BNCS treatment would consist of an intra-articular injection of boron followed by neutron irradiation of the joint. Monte Carlo radiation transport calculations have been used to develop an accelerator-based epithermal neutron beam line for BNCS treatments. The model includes a moderator/reflector assembly, neutron producing target, target cooling system, and arthritic joint phantom. Single and parallel opposed beam irradiations have been modeled for the human knee, human finger, and rabbit knee joints. Additional reflectors, placed to the side and back of the joint, have been added to the model and have been shown to improve treatment times and skin doses by about a factor of 2. Several neutron-producing charged particle reactions have been examined for BNCS, including the 9Be(p,n) reaction at proton energies of 4 and 3.7 MeV, the 9Be(d,n) reaction at deuteron energies of 1.5 and 2.6 MeV, and the 7Li(p,n) reaction at a proton energy of 2.5 MeV. For an accelerator beam current of 1 mA and synovial boron uptake of 1000 ppm, the time to deliver a therapy dose of 10,000 RBEcGy ranges from 3 to 48 min, depending on the treated joint and the neutron producing charged particle reaction. The whole-body effective dose that a human would incur during a knee treatment has been estimated to be 3.6 rem or 0.75 rem, for 1000 ppm or 19,000 ppm synovial boron uptake, respectively, although the shielding configuration has not yet been optimized. The Monte Carlo design process culminated in the construction, installation, and testing of a dedicated BNCS beam line on the high-current tandem electrostatic accelerator at the Laboratory for Accelerator Beam Applications at the Massachusetts Institute of Technology.