Several researchers recently demonstrated that it is feasible to locate building occupants solely from measured footstep vibrations. The research reported here applies that capability to track multiple building occupants in motion. In contrast to many indoor tracking methods based on wireless technology, this method frees individuals from the need to carry a device, and, furthermore, permits localization and tracking in facilities that restrict or prohibit wireless devices or cameras. Another consideration is that no personally-identifiable information needs to be disclosed as in the case of camera-based tracking. The proposed tracking algorithm addresses the issue of correct footstep-to-building occupant association and of handling missing detections or false alarms. A demonstration with actual measurements from a public building illustrates the operation of the algorithm.