A computer program was developed during the course of this work to calculate electron arc dose distributions with the angle $ beta$ concept. The angle $ beta$ uniquely describes the dependence of radial percentage depth doses an electron arc therapy on the nominal field width, isocenter depth, and virtual source-axis distance. The $ beta$ concept can be used in clinical situations to determine the field width when the isocenter depth and the required radial percentage depth dose are known. This thesis presents an overview of the physical properties of electron arc therapy and describes in detail the angle $ beta$ pseudo-arc technique used at McGill. A description of the algorithms used in the computer program is given the $ beta$ technique is compared to measurements and other calculation methods.