We report on a novel, non-invasive patient positioning system for radiosurgery of extracranial tumors. The system consisted of infrared cameras and reflective markers attached to the skin. Because localization accuracy is critical in radiosurgery, we performed a theoretical analysis of the accuracy of the system. A computer simulation program modeled errors in marker position, and was used to predict errors in targeting and study methods for minimizing errors. The use of redundant markers improved the overall accuracy of targeting. Experimental data was collected using a rigid torso phantom and correlated with theoretical results. The accuracy of the infrared system was compared with existing systems.