Detection of human respiration and heartbeat is an essential demand in medical monitoring, healthcare vigilance, as well as in rescue activities after earthquakes. Radar is an important tool to detect human respiration and heartbeat. Compared to body-attached sensors, radar has the advantage of conducting detection without contacting the subject, which is favorable in practical usage. In this paper, we conduct fundamental studies on ultra-wideband (UWB) radar for detection of the respiration and heartbeat by computer simulations. The main achievement of our work is the development of a UWB radar simulation system. Using the developed simulation system, three UWB frequency bands, i.e., 3.4-4.8GHz, 7.25-10.25GHz, as well as 3.1-10.6GHz, are compared in terms of their respiration and heartbeat detection performance. Our results show that the first two bands present identical performance, while the third one presents much better performance. The effects of using multiple antennas are also evaluated. Our results show that increasing the number of antennas can steadily increase the detection ability.