In this thesis results are presented from a study of the off-axis X and Gamma radiation field caused by a highly relativistic electron beam in liquid Nitrogen at various path lengths out to 2 radiation lengths. The off-axis dose in Silicon was calculated using electron/photon transport code CYLTRAN and measured using thermal luminescent dosimeters (TLD's). Calculations were performed on a CDC-7600 computer ar Los Alamos National Laboratory and measurements were made using the Naval Postgraduate School 100 Mev Linac. Comparison of the results is made and CYLTRAN is found to be in agreement with experimentally measured values. The CYLTRAN results are extended to the off-axis dose caused by a 100 Mev electron beam in air at Standard Temperature and Pressure (STP)