Recent advances in immunological technology have made it feasible to investigate the diagnosis and treatment of cancer with radiolabelled anti-tumor antibodies. The red bone marrow and endosteal cells of bone are likely to be the dose limiting tissues for systemic applications. Therefore, it is of clinical importance to quantitate their dose. Due to the small size of the marrow cavities in trabecular bone, it is experimentally difficult to measure the electron dose distribution. A computer simulation of electron transport is used to determine the dose distribution inside the marrow cavity. Electrons are backscattered more from bone than soft tissue, thereby increasing the dose to the radiosensitive endosteum and red bone marrow. A point source of beta activity (204Tl and 147pm) sandwiched between planar slabs of bone and red bone marrow equivalent plastics and 7LiF thermoluminescent dosimeters (TLD's) were used to determine the dose increase at various distances from the interface. Experimental results were compared with calculations using the Monte Carlo codes EGS (Electron Gamma Shower, SLAC) and CYLTRAN (Oak Ridge National Laboratory). The planar geometry was used as a benchmark geometry to compare the computer codes with experiment. After checking the accuracy of the codes for low energy electron transport, ACCEPT, a version of CYLTRAN, was used to investigate the radiation dose increase due to a point source of beta activity inside a polystyrene sphere bounded by aluminum. Spheres with radii of 200 and 500 microns were used. / Thesis / Master of Science (MS)