This clinical trial studies the side effects of computed tomography (CT)-guided stereotactic body radiation therapy (SBRT) with intrafraction motion monitoring and to see how well it works in treating patients with prostate cancer that has not spread to other parts of the body (localized). In CT-guided SBRT, x-ray-based imaging and cone-beam CTs are used to define and localize the area to be treated with SBRT. SBRT is a type of external radiation therapy that uses special equipment to position a patient and precisely deliver radiation to tumors in the body (except the brain). The total dose of radiation is divided into smaller doses given over several days. This type of radiation therapy helps spare normal tissue. A recent randomized trial showed that while SBRT is associated with less urinary incontinence and erectile dysfunction than complete surgical removal of the prostate, there are more urinary irritative side effects and more bowel side effects than with surgery. One source of uncertainty in SBRT that may contribute to genitourinary (GU) and gastrointestinal (GI) side effects is the necessity of treating a margin of volume around the prostate to account for its movement during SBRT. Intrafraction motion monitoring is any technique or system designed to track the movement of the body and target during fractions of external beam radiation to keep the beam on target. This allows for the patient to be repositioned, if needed, to ensure delivery of the SBRT to only the planned treatment area. CT-guided SBRT with intrafraction motion monitoring may lower GU and GI side effects by allowing tighter margins, as has been demonstrated with magnetic resonance imaging (MRI)-guided SBRT.