The use of high energy linear accelerators for radiation therapy has given rise to an unexpected Health Physics concern. These accelerators are designed to produce electrons or photons in excess of 10 MeV. In recent years it has been noted that these accelerators are producing significant fluences of high energy neutrons which contribute greatly to the dose equivalent received by technicians and others in areas adjacent to treatment rooms. Proper shielding of these neutron fluences requires knowledge of the neutron spectrum at barriers to the treatment room. The present paper presents one method by which the neutron spectrum may be unfolded. The method makes use of Bonner Sphere data and matrix inversion computer codes to approximate the spectrum of neutrons produced by medical linear accelerators.