Humans are made up of mostly soft tissue that vibrates during locomotion. This vibration has been shown to store and dissipate energy during locomotion. However, the effects of soft tissue vibration (wobbling masses) on the dynamics of bipedal walking have not been assessed in terms of stability. Given that much of the human body is vibrating just following foot-ground contact, it may have dynamic implications on the stability of walking. A rigid bipedal walker and a bipedal walker with soft tissue were simulated to quantify the effects of soft tissue vibration on gait periodicity, orbital stability, global stability, and robustness to uneven terrain. It was found that moderate amounts of energy dissipation resulted in much more stable walking dynamics relative to that of a rigid bipedal walker.