The dose distribution of a therapeutic photon or electron beam in the vicinity of a medium interface (muscle/bone, tissue/lung, tissue/shielding or medium/dosimeter) is affected by the exchange of scattered photons, scattered electrons and bremsstrahlung photons between the medium with the higher atomic number and the medium with the lower atomic number. In the case of a shielding interface in tissue, a therapeutic electron beam dose distribution can be enhanced by 20 to 60%, and the perturbation can be detected several cm from the interface. In this research project we will develop mathematical models to describe the perturbation of photon and electron beam dose distributions in the vicinity of single interfaces, multiple interfaces, interfaces that may be parallel to or at an angle to the beam axis and interfaces having cylindrical or spherical symmetry. For electron beams, this work will result in improvements in theory of beam spreading, depth dose curves, the effects of collimator scatter, and in the definition of effective depth. The research program will investigate the following major components of electron beams: 1) the primary electrons (using the fluence transformation method), 2) the diffusion electrons (which originate in the primary distribution), 3) the secondary electrons, 4) the bremsstrahlung photons. For photon beams: 1) the distribution of scattered photons, and 2) the electrons set in motion by the photons. Comparisons with dose perturbation measurements already reported in the literature and further experimental and Monte Carlo verification will be made.