Participants will receive standard radiation therapy for prostate cancer-5 consecutive days for 8 weeks-in the National Institutes of Health (NIH) Radiation Oncology Clinic. Amifostine will be placed in the rectum by a mini-enema before each radiation treatment so that it covers the lining of the rectum. To determine the side effects of the treatment, patients will undergo a proctoscopic examination before beginning radiation therapy, two times during therapy, and at each follow-up visit for 5 years after treatment ends. This examination involves inserting a proctoscope (a thin flexible tube with a light at the end) into the rectum and taking pictures.