With the decreasing cost of monoclonal antibody production, radioimmunotherapy (RIT) has rapidly emerged as one of the more promising methods of treating cancer cells. RIT makes use of radio-labeled monoclonal antibodies to detect and deliver controlled doses of radiation to malignant cells. The primary advantage of this method is that damage to normal, healthy tissue is minimized. We investigated the use of radio-labeled antibodies as a method of tumor destruction. Our primary interests were the rate of antibody diffusion into the tumor, the antibody binding kinetics, and the overall effectiveness of radioimmunotherapy given the rate of radioactive decay. By modeling the concentration of bound antibody with respect to time, we were able to optimize tumor destruction while minimizing the damage to the surrounding tissue. Our results show that a computer simulation using FIDAP is a time-saving, cost-effective method of obtaining quantitative results about the binding kinetics of antibody to tumor. In addition, we determined that while the binding specificity plays an important role in ensuring proper binding to the tumor, the rate of antibody to antigen complex formation does not affect the treatment and that this process is limited by diffusion. Given this fact, we recommend that low molecular weight antibodies be used because they will typically have higher diffusivities. In an example case of metastatic melanoma, we found that 4.33 mg of 188Re-6D2 complex would destroy the tumor in our model.